Radiomic signature of a perivascular region

ABSTRACT

A method for characterising a perivascular region using medical imaging data of a subject. The method comprises calculating the value of a radiomic signature of the perivascular region using the medical imaging data. Also disclosed is a method for deriving a radiomic signature for predicting cardiovascular risk. The method comprises obtaining a radiomic dataset and using the radiomic dataset to construct a perivascular radiomic signature. Also disclosed are systems for performing the aforementioned methods.

FIELD OF THE INVENTION

The invention relates to methods of characterising a perivascularregion, in particular using a radiomic signature, and systems for thesame. The invention also relates to methods of deriving such signatures,and systems for the same.

BACKGROUND

Coronary artery disease (CAD) remains a major, leading cause ofmorbidity and mortality, despite significant advances in both primaryand secondary cardiovascular prevention. Non-invasive diagnostic teststo assess the presence of CAD in patients presenting with typical oratypical symptoms, such as coronary computed tomography angiography(CCTA), are the pillars of modern cardiovascular diagnostics, especially among individuals with low to mid pre-test likelihood of CAD.Such techniques traditionally rely on the detection of obstructivelesions or the presence and extent of coronary calcification forcardiovascular risk stratification. However, a significant number ofpatients have elevated residual cardiovascular risk despite optimalmedical therapy. Residual vascular inflammation in particular is adriver of adverse events, contributing to both atherosclerotic plaqueformation and destabilization, but may be hard to diagnose usingconventional tests, such as circulating inflammatory biomarkers that arenon-specific to vascular disease.

Interpretation of clinical imaging studies has traditionally relied on asubjective, operator-dependent, qualitative assessment of the imagedanatomy. This approach, although useful in the busy clinical setting,disregards the large amount of information that is included in allclinical scans.

WO 2016/024128 A1 and WO 2018/078395 A1 define a specific CCTA-basedmetric, namely the Fat Attenuation Index (FAI) or perivascular FAI(FAI_(PVAT)), which reflects the standardized, weighted averageattenuation of a perivascular region around the human coronary arteries,which was found to be a sensitive and dynamic biomarker of coronaryinflammation, and was subsequently identified as a strong andindependent predictor of adverse cardiac events. In the presence ofvascular inflammation, the release of pro-inflammatory molecules fromthe diseased vascular wall inhibits differentiation and lipidaccumulation in pre-adipocytes within the perivascular tissue (PVT),resulting in smaller, less differentiated and lipid-free adipocytecells. This is associated with a shift in the radiodensity (measured asattenuation values) of PTV in computed tomography (CT) imaging from morenegative (closer to −190) to less negative (closer to −30) HounsfieldUnit (HU) values, which may be captured by the FAI. While both thebiological meaning and clinical value of the FAI have been extensivelyvalidated, it does not adequate describe the full range of phenotypicvariability observed in coronary PVT.

In a recent study, Kolossvary et al. showed that radiomic features canreliably identify plaques with the high-risk plaque feature napkin-ringsign, the identification of which normally relies on a qualitativeassessment of plaque anatomy and the experienced eye of the operator(Kolossvary M, Karady J, Szilveszter B, et al. Radiomic Features AreSuperior to Conventional Quantitative Computed Tomographic Metrics toIdentify Coronary Plaques With Napkin-Ring Sign. Circ Cardiovasc Imaging2017; 10(12): e006843). However, this approach focuses on phenotyping ofthe plaques themselves and neglects the PVT and the valuable informationthat can be gained therefrom.

What is needed is a method or tool that provides prognostic value forcardiovascular risk over and above current CCTA-based riskstratification tools, such as the presence and extent of CAD, presenceof high-risk plaque features, coronary calcium and the recentlydescribed FAI_(PVAT).

SUMMARY OF THE INVENTION

According to a first aspect of the invention, there is provided a methodfor characterising a perivascular region (for example its phenotype,e.g. composition and/or texture) using medical imaging data of asubject. The method may comprise calculating the value of a radiomicsignature of the perivascular region using the medical imaging data. Theradiomic signature may be calculated on the basis of measured values ofat least two radiomic features of the perivascular region. The measuredvalues of the at least two radiomic features may be calculated from orusing the medical imaging data.

The radiomic signature may provide a measure of the texture of theperivascular region.

At least one of the at least two radiomic features may provide a measureof the texture of the perivascular region.

The radiomic signature may be predictive of cardiovascular risk.

The radiomic signature may be predictive of the likelihood of thesubject experiencing a major adverse cardiovascular event.

The radiomic signature may be predictive of the likelihood of thesubject experiencing a cardiac-specific major adverse cardiovascularevent.

The radiomic signature may be indicative of cardiovascular health.

The radiomic signature may be indicative of vascular disease. Forexample, the radiomic feature may be indicative of vascularinflammation.

At least one of the at least two radiomic features may be calculatedfrom a wavelet transformation of the attenuation values.

Each of the at least two radiomic features may be volume-independentand/or orientation-independent.

The at least two radiomic features may be selected from the radiomicfeatures of clusters 1 to 9, wherein the at least two radiomic featuresare each selected from different clusters, wherein:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, High Gray Level Run Emphasis,        Autocorrelation, Sum Average, Joint Average, and High Gray Level        Zone Emphasis;    -   cluster 2 consists of Skewness, Skewness LLL, Kurtosis, 90th        Percentile, 90th Percentile LLL, Median LLL, Kurtosis LLL, and        Median;    -   cluster 3 consists of Run Entropy, Dependence Entropy LLL,        Dependence Entropy, Zone Entropy LLL, Run Entropy LLL, and Mean        LLL;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, Low        Gray Level Zone Emphasis, Short Run Low Gray Level Emphasis, Low        Gray Level Run Emphasis, Low Gray Level Emphasis, Small        Dependence Low Gray Level Emphasis, Gray Level Variance LLL        (GLSZM), Gray Level Variance (GLDM), Variance, Gray Level        Variance (GLDM), Difference Variance LLL, Gray Level Variance        LLL (GLRLM), Variance LLL, Gray Level Variance LLL (GLDM), Sum        of Squares, Contrast LLL, Mean Absolute Deviation, Interquartile        Range, Robust Mean Absolute Deviation, Long Run Low Gray Level        Emphasis, Difference Variance, Gray Level Variance (GLSZM),        Inverse Difference Moment Normalized, Mean Absolute Deviation        LLL, Sum of Squares LLL, and Contrast;    -   cluster 5 consists of Zone Entropy, Gray Level Non Uniformity        Normalized (GLRLM), Gray Level Non Uniformity Normalized LLL        (GLRLM), Sum Entropy, Joint Energy, Entropy, Gray Level Non        Uniformity Normalized (GLDM), Joint Energy, Gray Level Non        Uniformity Normalized LLL (GLDM), Uniformity LLL, Sum Entropy        LLL, and Uniformity;    -   cluster 6 consists of Zone Entropy HHH, Size Zone Non Uniformity        Normalized HHH, and Small Area Emphasis HHH;    -   cluster 7 consists of Strength, Coarseness HLL, Coarseness,        Coarseness LHL, Coarseness LLL, Coarseness LLH, Coarseness HHH,        Coarseness HLH, Coarseness HHL, and Coarseness LHH;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, Sum Entropy,        Interquartile Range, Cluster Prominence LLL, Entropy LLL, 10th        Percentile LLL, 10th Percentile; and    -   cluster 9 consists of Size Zone Non Uniformity LLL, Dependence        Non Uniformity HLL, Gray Level Non Uniformity HLL (GLSZM), Gray        Level Non Uniformity (GLSZM), Run Length Non Uniformity HHL, Run        Length Non Uniformity LHL, Dependence Non Uniformity LHL,        Dependence Non Uniformity, Run Length Non Uniformity HLH,        Busyness, Run Length Non Uniformity LLH, Dependence Non        Uniformity LLH, Dependence Non Uniformity LLL, Size Zone Non        Uniformity, Energy HLL, Run Length Non Uniformity LHH, Size Zone        Non Uniformity HLL, Gray Level Non Uniformity LLH (GLSZM), Gray        Level Non Uniformity LHL (GLSZM), Gray Level Non Uniformity LLL        (GLSZM), Run Length Non Uniformity HLL, Gray Level Non        Uniformity HLH (GLSZM), Gray Level Non Uniformity HHL (GLSZM),        Run Length Non Uniformity, and Run Length Non Uniformity HHH.

Clusters 1 to 9 may instead be defined as follows:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, High Gray Level Run Emphasis,        Autocorrelation, Sum Average, and Joint Average;    -   cluster 2 consists of Skewness, Skewness LLL, Kurtosis, 90th        Percentile, 90th Percentile LLL, Median LLL, and Kurtosis LLL;    -   cluster 3 consists of Run Entropy, Dependence Entropy LLL,        Dependence Entropy, and Zone Entropy LLL;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, Low        Gray Level Zone Emphasis, Short Run Low Gray Level Emphasis, Low        Gray Level Run Emphasis, Low Gray Level Emphasis, Small        Dependence Low Gray Level Emphasis, Gray Level Variance LLL        (GLSZM), Gray Level Variance (GLDM), Variance, Gray Level        Variance (GLDM), and Difference Variance LLL;    -   cluster 5 consists of Zone Entropy, Gray Level Non Uniformity        Normalized (GLRLM), and Gray Level Non Uniformity Normalized LLL        (GLRLM);    -   cluster 6 consists of Zone Entropy HHH, and Size Zone Non        Uniformity Normalized HHH;    -   cluster 7 consists of Strength, Coarseness HLL, Coarseness,        Coarseness LHL, Coarseness LLL, Coarseness LLH, and Coarseness        HHH;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, Sum Entropy,        Interquartile Range, Cluster Prominence LLL, Entropy LLL, 10th        Percentile LLL, and 10th Percentile; and    -   cluster 9 consists of Size Zone Non Uniformity LLL, Dependence        Non Uniformity HLL, Gray Level Non Uniformity HLL (GLSZM), Gray        Level Non Uniformity (GLSZM), Run Length Non Uniformity HHL, Run        Length Non Uniformity LHL, Dependence Non Uniformity LHL,        Dependence Non Uniformity, Run Length Non Uniformity HLH,        Busyness, Run Length Non Uniformity LLH, Dependence Non        Uniformity LLH, Dependence Non Uniformity LLL, Size Zone Non        Uniformity, Energy HLL, Run Length Non Uniformity LHH, Size Zone        Non Uniformity HLL, Gray Level Non Uniformity LLH (GLSZM), and        Gray Level Non Uniformity LHL (GLSZM).

Clusters 1 to 9 may instead be defined as follows:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, High Gray Level Run Emphasis,        Autocorrelation, Sum Average, and Joint Average;    -   cluster 2 consists of Skewness, Skewness LLL, Kurtosis, and 90th        Percentile;    -   cluster 3 consists of Run Entropy, Dependence Entropy LLL, and        Dependence Entropy;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, Low        Gray Level Zone Emphasis, Short Run Low Gray Level Emphasis, Low        Gray Level Run Emphasis, Low Gray Level Emphasis, and Small        Dependence Low Gray Level Emphasis;    -   cluster 5 consists of Zone Entropy, and Gray Level Non        Uniformity Normalized (GLRLM);    -   cluster 6 consists of Zone Entropy HHH;    -   cluster 7 consists of Strength, Coarseness HLL, Coarseness,        Coarseness LHL, Coarseness LLL, and Coarseness LLH;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, Sum Entropy,        Interquartile Range, Cluster Prominence LLL, Entropy LLL, 10th        Percentile LLL, and 10th Percentile; and cluster 9 consists of        Size Zone Non Uniformity LLL, Dependence Non Uniformity HLL,        Gray Level Non Uniformity HLL (GLSZM), Gray Level Non Uniformity        (GLSZM), Run Length Non Uniformity HHL, Run Length Non        Uniformity LHL, Dependence Non Uniformity LHL, Dependence Non        Uniformity, Run Length Non Uniformity HLH, Busyness, Run Length        Non Uniformity LLH, Dependence Non Uniformity LLH, Dependence        Non Uniformity LLL, and Size Zone Non Uniformity.

Clusters 1 to 9 may instead be defined as follows:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, High Gray Level Run Emphasis, and        Autocorrelation;    -   cluster 2 consists of Skewness, and Skewness LLL;    -   cluster 3 consists of Run Entropy, and Dependence Entropy LLL;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, and        Low Gray Level Zone Emphasis;    -   cluster 5 consists of Zone Entropy;    -   cluster 6 consists of Zone Entropy HHH;    -   cluster 7 consists of Strength;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, Sum Entropy,        Interquartile Range, Cluster Prominence LLL, Entropy LLL, 10th        Percentile LLL, and 10th Percentile; and cluster 9 consists of        Size Zone Non Uniformity LLL, Dependence Non Uniformity HLL,        Gray Level Non Uniformity HLL (GLSZM), Gray Level Non Uniformity        (GLSZM), Run Length Non Uniformity HHL, and Run Length Non        Uniformity LHL.

Clusters 1 to 9 may instead be defined as follows:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, and High Gray Level Run Emphasis;    -   cluster 2 consists of Skewness, and Skewness LLL;    -   cluster 3 consists of Run Entropy;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, and        Low Gray Level Zone Emphasis;    -   cluster 5 consists of Zone Entropy;    -   cluster 6 consists of Zone Entropy HHH;    -   cluster 7 consists of Strength;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, and Sum Entropy; and        cluster 9 consists of Size Zone Non Uniformity LLL.

Clusters 1 to 9 may instead be defined as follows:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, and High Gray Level Run Emphasis;    -   cluster 2 consists of Skewness, Skewness LLL, Kurtosis, 90th        Percentile, Median LLL, Kurtosis LLL, and Median;    -   cluster 3 consists of Run Entropy, Run Entropy LLL, and Mean        LLL;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, Low        Gray Level Zone Emphasis, and Gray Level Variance (GLSZM);    -   cluster 5 consists of Zone Entropy, Gray Level Non Uniformity        Normalized (GLRLM), and Uniformity;    -   cluster 6 consists of Zone Entropy HHH;    -   cluster 7 consists of Strength;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Mean Absolute Deviation LLL, Gray Level Variance LLL (GLDM),        Variance LLL, Gray Level Variance LLL (GLRLM), Robust Mean        Absolute Deviation LLL, Gray Level Variance LLL (GLSZM),        Interquartile Range LLL, Sum Entropy LLL, Gray Level Variance        (GLRLM), Variance, Gray Level Variance (GLDM), Mean Absolute        Deviation, Sum Entropy, Robust Mean Absolute Deviation,        Interquartile Range, Entropy LLL, 10th Percentile LLL, 10th        Percentile, Entropy, Uniformity LLL, Gray Level Non Uniformity        Normalized LLL (GLDM), Gray Level Non Uniformity Normalized LLL        (GLRLM), Root Mean Squared, Gray Level Non Uniformity Normalized        (GLDM), Root Mean Squared LLL, and Long Run Low Gray Level        Emphasis; and cluster 9 consists of Size Zone Non Uniformity        LLL, Busyness, and Size Zone Non Uniformity.

The at least two radiomic features may be selected from: Median LLL,Mean LLL, Median, Root Mean Squared LLL, Mean, Kurtosis, Root MeanSquared, Run Entropy LLL (GLRLM), Uniformity, 90th Percentile, GrayLevel Non-Uniformity Normalized (GLRLM), Uniformity LLL, Skewness, GrayLevel Non-Uniformity Normalized LLL (GLRLM), 10th Percentile LLL,Skewness LLL, 10th Percentile, Entropy, Interquartile Range LLL, RobustMean Absolute Deviation LLL, Run Entropy (GLRLM), Interquartile Range,Sum Entropy (GLCM), Gray Level Non-Uniformity Normalized LLL (GLRLM),Dependence Non-Uniformity LHL (GLDM), Kurtosis LLL, Run LengthNon-Uniformity HHL (GLRLM), Entropy LLL, Robust Mean Absolute Deviation,Sum Entropy LLL (GLCM), 90th Percentile LLL, Run Entropy HHL (GLRLM),Energy, Energy LLL, Strength (NGTDM), Autocorrelation (GLCM), MeanAbsolute Deviation LLL, High Gray Level Emphasis (GLDM), Joint Average(GLCM), Sum Average (GLCM), Short Run High Gray Level Emphasis (GLRLM),Energy HHH, High Gray Level Run Emphasis (GLRLM), Run Entropy HHH(GLRLM), Energy HHL, and Mean Absolute Deviation.

The at least two radiomic features may be selected from the radiomicfeatures of clusters 1 to 8. The at least two radiomic features may beselected from the radiomic features of clusters 1 to 7. The at least tworadiomic features may be selected from the radiomic features of clusters1 to 6. The at least two radiomic features may be selected from theradiomic features of clusters 1 to 5. The at least two radiomic featuresmay be selected from the radiomic features of clusters 1 to 4. The atleast two radiomic features may be selected from the radiomic featuresof clusters 1 to 3. The at least two radiomic features may be selectedfrom the radiomic features of clusters 1 and 2.

The at least two radiomic features may comprise at least three radiomicfeatures. The at least two radiomic features may comprise at least fourradiomic features. The at least two radiomic features may comprise atleast five radiomic features. The at least two radiomic features maycomprise at least six radiomic features. The at least two radiomicfeatures may comprise at least seven radiomic features. The at least tworadiomic features may comprise at least eight radiomic features. The atleast two radiomic features may comprise at least nine radiomicfeatures.

The at least two radiomic features may comprise six radiomic features,wherein the six radiomic features are Short Run High Gray LevelEmphasis, Skewness, Run Entropy, Small Area Low Gray Level Emphasis,Zone Entropy HHH, and Zone Entropy.

The at least two radiomic features may comprise nine radiomic features,wherein the nine radiomic features are Short Run High Gray LevelEmphasis, Skewness, Run Entropy, Small Area Low Gray Level Emphasis,Zone Entropy HHH, Zone Entropy, Strength, Cluster Tendency LLL, and SizeZone Non Uniformity.

The radiomic signature may comprise a weighted sum of the values of eachof the at least two radiomic features. The radiomic signature may belinearly related to the weighted sum of the values of each of the atleast two radiomic features.

The medical imaging data may comprise attenuation values for each of aplurality of voxels corresponding to at least the perivascular region.The plurality of voxels may also correspond to the blood vessel aroundwhich the perivascular region is disposed.

The method may further comprise identifying the perivascular region (orsubstance, tissue or type of perivascular tissue, for example adiposetissue) using the medical imaging data. The perivascular region may beidentified as all voxels of the medical imaging data having anattenuation (or radiodensity) value falling within a given range ofattenuation values and/or located within a given radial distance from anouter vessel wall (i.e. the vessel adjacent to the perivascular tissue).The given range of attenuation values may be from about −190 to about−30 Hounsfield Units, for example if the perivascular region correspondsto perivascular adipose tissue. The given range of attenuation valuesmay be from about −30 to about +30 Hounsfield Units, for example if theperivascular region corresponds to water. The given radial distance maybe a distance related to one or more dimensions of the adjacent vessel.The given radial distance may be equal to the diameter of the adjacentvessel. The given radial distance may be a fixed value, for example 5mm.

The perivascular region may be adjacent to or surround a coronaryartery, carotid artery, aorta or any other artery in the human body. Forexample, the perivascular region may be adjacent to or surround theproximal and/or mid right coronary artery. The method may furthercomprise segmenting the perivascular region. The method may furthercomprise calculating the values of the radiomic features from thesegmented perivascular region.

The values of each of the at least two radiomic features may becalculated from raw attenuation values, binned attenuation values, or awavelet transformation of the attenuation values.

The method may further comprise predicting the risk of the subjectexperiencing a major adverse cardiac event based on the calculated valueof the radiomic signature.

The method may further comprise predicting the risk of the subjectexperiencing a cardiac-specific major adverse cardiac event based on thecalculated value of the radiomic signature.

The method may further comprise determining whether the subject hasvascular disease based on the calculated value of the radiomicsignature. The vascular disease may be selected from the groupconsisting of atherosclerosis, vascular calcification, intimahyperplasia, vascular aneurysm and vascular inflammation.

The method may further comprise determining whether the subject hascoronary heart disease based on the calculated value of the radiomicsignature.

The calculated value of the radiomic signature may be used todiscriminate unstable from stable coronary lesions. The perivascularregion may be a peri-lesion region.

According to a second aspect of the invention, there is provided methodfor deriving a radiomic signature for predicting cardiovascular risk.The method may comprise using a dataset, for example a radiomic dataset,to construct a perivascular radiomic signature or score for predictingcardiovascular risk. The radiomic signature may be calculated on thebasis of at least two radiomic features of a perivascular region. Thedataset may comprise the measured values of a plurality of radiomicfeatures of a perivascular region obtained from medical imaging data foreach of a plurality of individuals. The plurality of individuals maycomprise a first group of individuals having reached a clinical endpointindicative of cardiovascular risk and a second group of individualshaving not reached a clinical endpoint indicative of cardiovascularrisk.

The first group of individuals may have reached a clinical endpointindicative of cardiovascular risk within a subsequent period after themedical imaging data were collected and a second group of individualsmay not have reached a clinical endpoint indicative of cardiovascularrisk within the subsequent period after the medical imaging data werecollected.

Each of the at least two radiomic features may be selected to becollinear (or correlated) with a corresponding partner radiomic featurethat is significantly (i.e. statistically significant) associated withthe clinical endpoint, for example as determined or calculated from thedataset. The partner radiomic features of the at least two radiomicfeatures may each be different to one another.

Each of the at least two radiomic features may be selected to be, or tobe collinear with, different significant radiomic features that aresignificantly associated with the clinical endpoint (as determined fromthe dataset, i.e. identified from the dataset as being significantlyassociated with the clinical endpoint). The method may thereforecomprise identifying significant radiomic features from amongst theplurality of radiomic features that are each significantly associatedwith the clinical endpoint, the at least two radiomic features eachbeing selected to be, or to be collinear with, different significantradiomic features.

The significant radiomic features may be selected to be not collinearwith each other. For example, the method may further compriseidentifying a subset of the plurality of radiomic features (e.g. asubset of the significant radiomic features) that are not collinear witheach other, the at least two radiomic features each being selected tobe, or to be collinear with, different radiomic features belonging tothe subset.

Each of the partner radiomic features may be selected to be notcollinear with any of the other partner radiomic features.

At least one of the at least two radiomic features may be its ownpartner radiomic feature.

Each of the at least two radiomic features may be selected to besignificantly associated with the clinical endpoint, for example asdetermined or calculated from the dataset.

The method may comprise identifying a plurality of clusters of radiomicfeatures. Each cluster may comprise a subset of the plurality ofradiomic features. Each cluster may include an original radiomic featurewith which each of the other radiomic features in that cluster isselected to be collinear, for example as determined or calculated fromthe dataset. The at least two radiomic features may each be selectedfrom different clusters.

Each of the original radiomic features may be selected to be notcollinear with any of the original radiomic features of any of the otherclusters, for example as determined or calculated from the dataset.

Each of the radiomic features in each cluster may be selected to becollinear with all of the other radiomic features in the same cluster,for example as determined or calculated from the dataset.

Each of the original radiomic features may be selected to besignificantly associated with the clinical endpoint, for example asdetermined or calculated from the dataset.

Each of the original radiomic features may be selected to be the moststrongly associated with the clinical endpoint of all the radiomicfeatures in its cluster, for example as determined or calculated fromthe dataset.

The at least two radiomic features may be selected to be not collinearwith each other, for example as determined or calculated from thedataset.

Two radiomic features may be identified as collinear if they arecorrelated to an extent greater than a correlation threshold.

The collinearity between radiomic features may be calculated usingSpearman's rho coefficient. Alternatively, collinearity between radiomicfeatures may be calculated using other measures of pairwise correlation,such as Pearson's correlation coefficient (Pearson's r).

The correlation threshold may be at least about 10.751, for exampleabout |rho|=0.75.

A radiomic feature may be identified as being significantly associatedwith the clinical endpoint if it is associated with the clinicalendpoint above a significance threshold, for example as determined orcalculated from the dataset. The significance threshold may be at leastabout α=0.05, e.g. about α=0.05.

The association of the radiomic features with the clinical endpoint maybe calculated based on a receiver operating characteristic (ROC) curveanalysis, in particular using an area under the curve (AUC) measurement(i.e. the C-statistic), as will be readily understood by those skilledin the art.

A Bonferroni correction may be applied to the significance threshold.

A principal component analysis of the plurality of radiomic features maybe performed, for example using the dataset (specifically on the valuesof the radiomic features of the plurality of individuals). TheBonferroni correction may be based on the number of principal componentsthat account for a given amount of the observed variation, as determinedfrom the principal component analysis. The given amount of observedvariation may be at least about 99.5%, for example about 99.5%.

The radiomic signature may be constructed to be correlated with theclinical endpoint. The radiomic signature may be constructed to besignificantly associated with the clinical endpoint.

The radiomic signature may be identified as being significantlyassociated with the clinical endpoint if it is associated with theclinical endpoint above a significance threshold, for example asdetermined or calculated from the dataset. The significance thresholdmay be at least about 0.05, e.g. about α=0.05.

The dataset may be divided into data for a training cohort ofindividuals and a validation cohort of individuals. The step ofconstructing the radiomic signature may comprise deriving the signatureusing data for at least the training cohort. The step of constructingthe radiomic signature may comprise validating the signature using datafor the validation cohort.

A radiomic feature may be identified as being significantly associatedwith the clinical endpoint only if it is significantly associated withthe clinical endpoint in both cohorts. The radiomic signature may beidentified as being significantly associated with the clinical endpointif it is significantly associated with the clinical endpoint in thetraining cohort.

Each of the at least two radiomic features may be volume-independent.Each of the at least two radiomic features may beorientation-independent. The plurality of radiomic features may each bevolume- and/or orientation-independent.

Any volume- and/or orientation-dependent radiomic features may beremoved from the plurality of radiomic features prior to selection ofthe at least two radiomic features.

The at least two radiomic features may be selected to be stable, forexample as determined or calculated from the dataset. For example, theat least two radiomic features may be selected from amongst those thatare identified as being stable, for example as determined or calculatedfrom the dataset.

All unstable features may be removed from the plurality of radiomicfeatures. For example, all unstable features may be removed from theplurality of radiomic features before the at least two radiomic featuresare selected.

A radiomic feature may be identified as being unstable if the intraclasscorrelation coefficient (ICC) for that radiomic feature (calculated forrepeat measurements or scans) is less than a stability threshold. Thestability threshold may be at least about 0.9, for example 0.9. Theintraclass correlation coefficient may be calculated based on theZ-scores (or standard score, i.e. expressed in terms of the number ofstandard deviations from the mean) of the radiomic features.

The step of constructing the radiomic signature may comprise refiningthe contribution of the at least two radiomic features to the radiomicsignature to increase the association or correlation of the radiomicsignature with the clinical endpoint. The radiomic signature may beconstructed to be significantly associated with the clinical endpoint.

The association of the radiomic signature with the clinical endpoint maybe calculated based on a receiver operating characteristic (ROC) curveanalysis, in particular using an area under the curve (AUC) measurement(i.e. the C-statistic), as will be readily understood by those skilledin the art.

The step of constructing the radiomic signature may be performed using amachine learning algorithm.

The step of constructing the radiomic signature may be performed usingleave-p-out internal cross-validation.

The step of constructing the radiomic signature may be performed usingleave-one-out internal cross-validation.

The step of constructing the radiomic signature may be performed usingelastic network regression.

The radiomic signature may comprise a weighted sum of the at least tworadiomic features.

The radiomic signature may be linearly related to the weighted sum ofthe at least two radiomic features.

The step of constructing the radiomic signature may comprise adjustingthe relative weightings of each of the at least two radiomic features toincrease the association or correlation of the radiomic signature withthe clinical endpoint.

The radiomic signature may be constructed to provide a measure of thetexture of the perivascular region.

At least one of the at least two radiomic features may provide a measureof the texture of the perivascular region. For example, each of the atleast two radiomic features may provide a measure of the texture of theperivascular region (i.e. each of the at least two radiomic features maybe texture statistics).

The clinical endpoint may be the composite endpoint of major adversecardiac events. The clinical endpoint may be the composite endpoint ofcardiac-specific major adverse cardiac events.

The methods of the invention may also comprise the step of calculatingthe radiomic features from the medical imaging data.

The radiomic signature of the invention may also be calculated on thebasis of further radiomic features in addition to the at least tworadiomic features referred to above.

Thus, it may be said that the radiomic signature is calculated on thebasis of a plurality of radiomic features, and the plurality of radiomicfeatures may comprise the at least two radiomic features. For example,the method for deriving a radiomic signature for predictingcardiovascular risk may comprise using a dataset, in particular aradiomic dataset, to construct a perivascular radiomic signature orscore for predicting cardiovascular risk. The radiomic signature may becalculated on the basis of a (second) plurality of perivascular radiomicfeatures (i.e. radiomic features of a perivascular region). The datasetmay comprise the measured values of a (first) plurality of perivascularradiomic features of a perivascular region obtained from medical imagingdata for each of a plurality of individuals. The plurality ofindividuals may comprise a first group of individuals having reached aclinical endpoint indicative of cardiovascular risk and a second groupof individuals having not reached a clinical endpoint indicative ofcardiovascular risk. The second plurality of perivascular radiomicfeatures may be selected from amongst the first plurality ofperivascular radiomic features, in particular to provide a radiomicsignature for predicting cardiovascular risk, as determined from orusing the dataset, for example using a machine learning algorithm. Theradiomic signature may therefore be calculated on the basis of furtherradiomic features (for example selected from the (first) plurality ofradiomic features) in addition to the at least two radiomic features.

The method may further comprise configuring a system for calculating thevalue of the radiomic signature for a patient. For example, the methodmay further comprise configuring a system for characterising aperivascular region of the patient or subject by calculating the valueof the derived radiomic signature for the patient or subject. The systemmay be configured to calculate the value of the derived radiomicsignature using or based on medical imaging data of at least aperivascular region of the patient or subject. The system may beconfigured to calculate the value of the derived radiomic signatureusing or based at least on the values of the at least two (or secondplurality) of radiomic features of the perivascular region of thepatient or subject.

The method may therefore be for deriving a perivascular radiomicsignature and configuring a system for characterising a perivascularregion of a patient using the derived radiomic signature.

The system may be configured to receive the medical imaging data orvalues of the at least two (or second plurality of) radiomic features asan input. The system may be configured to output (e.g. display) thecalculated value of the radiomic signature or a value based on thecalculated value of the radiomic signature. The system may be configuredto output an indication of the patient's cardiovascular risk and/orvascular health. The system may be configured to output an indication ofthe risk of the patient experiencing an adverse cardiovascular event.The system may be a computer system.

The method may comprise providing instructions for configuring a systemfor calculating the value of the derived radiomic signature for apatient or subject.

The method may further comprise calculating the value of the derivedradiomic signature for a perivascular region of a patient or subject.For example, the method may further comprise characterising aperivascular region of a patient or subject by calculating the value ofthe derived radiomic signature. The value of the derived radiomicsignature may be calculated based on or using medical imaging data of atleast the perivascular region of the patient or subject. The value ofthe derived radiomic signature may be calculated using or based at leaston the values of the at least two (or second plurality of) radiomicfeatures of the perivascular region of the patient or subject.

The method may therefore be for deriving a perivascular radiomicsignature and characterising a perivascular region using the derivedradiomic signature.

According to a third aspect of the invention, there is provided a systemconfigured to perform any of the methods as described above. The systemmay be a computer system. The system may comprise a processor configuredto perform the steps of the method. The system may comprise a memoryloaded with executable instructions for performing the steps of themethod.

According to a fourth aspect of the invention, there is provided use ofa perivascular radiomic signature for any of the above-describedpurposes, for example to characterise a perivascular region, to detectvascular disease, or to predict cardiovascular risk. The perivascularradiomic signature may be calculated on the basis of measured values ofa plurality of perivascular radiomic features of the perivascularregion.

The medical imaging data may be radiographic data. The medical imagingdata may be computed tomography data.

The perivascular region may be or may comprise perivascular tissue, forexample perivascular adipose tissue. The perivascular region may alsocomprise water, and/or other soft tissue structures within theperivascular region.

BRIEF DESCRIPTION OF THE FIGURES

The invention will now be described with reference to the appendedfigures, in which:

FIG. 1 illustrates the study methodology and design. FIG. 1A illustratesthe methodology of perivascular region phenotyping, volume segmentation,discretization, wavelet transformation and radiomic feature calculation.FIGS. 1B and 1C illustrate a summary of Arms 1 and 2 of the study,respectively. AMI: acute myocardial infarction; CAD: coronary arterydisease; CCTA: coronary computed tomography angiography; MACE: majoradverse cardiovascular events; PVR: perivascular region; H/L: high/lowwavelet transformation; VOI: volume of interest.

FIG. 2 summarises the building of the high-risk perivascular regionradiomic signature. FIG. 2A summarises the multi-step approach used tobuild the signature as a flow diagram. First, out of a total of 843calculated radiomic features, 124 were excluded following stabilityanalysis (ICC<0.9). Next, sixty radiomic features that weresignificantly associated with MACE at the level of α=0.05 in bothcohorts were selected. Among these, seven volume- andorientation-dependent features were excluded (e.g. Energy andnon-HHH/LLL transformations), and collinearity was subsequently reducedby stepwise elimination of pairwise correlations at the level of|rho|≥0.75. Using the remaining nine radiomic features, a machinelearning approach was applied in Cohort 1 using elastic networkregression and leave-one-out internal cross-validation. FIG. 2B showsthe relative variable importance (weighting) for the best performingmodel for prediction of MACE. FIG. 2C shows the relative variableimportance (weighting) for the best performing model for prediction ofcardiac-specific MACE (cMACE). The top six components of the model ofFIG. 2C were then used to define the Perivascular Texture Index (PTI),which is a radiomic signature according the invention. AUC: area underthe curve; CI: confidence interval; MACE: major adverse cardiovascularevents; SALGLE: small area low gray level emphasis; SRHGLE: short runhigh gray level emphasis; SZNU: size zone non-uniformity.

FIG. 3 shows that the PTI signature of the invention providesincremental prognostic information beyond current CCTA-based tools. In apooled analysis of both Arm 1 cohorts, addition of the perivasculartexture index (PTI) into a model consisting of age, sex, traditionalrisk factors and computed tomography-derived high-risk features,including pericoronary FAI_(PVAT), significantly improved the predictivevalue of the model for both MACE (δ[AUC]=0.020, P=0.014, FIG. 3A), andcardiac-specific MACE (δ[AUC]=0.046, P=0.012, FIG. 3B). Of note, PTI andFAI_(PVAT) were independently associated with the risk for bothendpoints, with higher values of both biomarkers linked to a higherprospective risk of adverse events. The interaction between the twoCT-derived perivascular region (PVR) features (PTI and FAI) is presentedgraphically in FIG. 3C using two-way contour plots depicting theadjusted probability for MACE (left) and cardiac-specific MACE (right)across different levels of the two biomarkers. These findings suggest asignificant clinical value for comprehensive phenotyping of coronaryperivascular region by means of both FAI_(PVAT) and PTI.

FIG. 4 shows a correlation plot of original radiomic features. Thecorrelation plot of the 107 coronary perivascular region radiomicfeatures shown was calculated from the original CCTA images. The plotdepicts the direction and strength of association between individualradiomic features (calculated by Spearman's rho coefficient) and revealsthe existence of distinct clusters of features.

FIG. 5 illustrates various aspects of the principal component analysisof coronary perivascular region radiomic features. FIG. 5A shows acomponent plot of the three major principal components in Arm 1. FIG. 5Bshows a scree plot depicting the percentage of variation explained bythe 92 first components, accounting for 99.5% of variation. FIG. 5Cshows a Manhattan plot for prediction of 5-year MACE for 42 componentswith eigenvalues >1. FIG. 5D shows a forest plot presenting the adjustedodds ratios (statistically adjusted for covariates such as age, gender)for prediction of 5-year MACE for the seven principal components thatwere significant in univariate analysis. FIG. 5E shows a correlationplot of selected components with demographics. FIG. 5F illustrates theincremental prognostic value of perivascular region radiomic componentsfor prediction of 5-year MACE. AUC: Area Under the Curve; BMI: body massindex; CCS: coronary calcium score; DM: diabetes mellitus; EAT:epicardial adipose tissue; HCH: hypercholesterolemia; HDL: high-densitylipoprotein; LDL: low-density lipoprotein; PC: principal component; PVR:perivascular region; SBP: systolic blood pressure; TG: triglyceride.

FIG. 6 shows a Manhattan plot for prediction of 5-year MACE. P valuesare derived from receiver operating characteristic (ROC) curve analysisfor discrimination of 5-year MACE, for all radiomic features calculatedon the original or wavelet-transformed images. MACE: major adversecardiovascular events; H/L: high/low signal pass in wavelettransformations.

FIG. 7 shows a plot of the intraclass correlation coefficient (ICC) ofall the perivascular region radiomic features. The radiomic features areranked according to the intraclass correlation coefficient (ICC) inrepeated analysis. A total of 719 radiomic features were found to haveICC≥0.9.

FIG. 8 shows that perivascular region texture phenotyping using aradiomic signature according to the invention may be used for detectionof unstable coronary lesions. FIGS. 8A-G show box and whisker plots thesix radiomic features included in the PTI and for the PTI itself. In Arm2, five out of the six constituent component radiomic features of thePTI were significantly altered in the presence of unstable versus stablecoronary lesions, while PTI outperformed all six individual radiomicfeatures in discriminating unstable form stable coronary lesions (AUC:0.76; 95% CI: 0.64-0.88). These findings suggest a close link betweenvascular inflammation associated with plaque rupture and perivascularregion texture changes (which can now be detected by the radiomicsignature of the invention, e.g. PTI) as a non-invasive way ofmonitoring the risk profile of a coronary lesion. AU: arbitrary units;SALGLE: small area low gray level emphasis; SRHGLE: short run high graylevel emphasis; SZNU: size zone non-uniformity.

DETAILED DESCRIPTION

The inventors have discovered that a perivascular region (PVR) radiomicsignature (otherwise known as a “score” or “index”) calculated on thebasis of two or more radiomic features of the PVR adds incremental valuebeyond traditional risk factors and established CCTA risk classificationtools in predicting future adverse cardiovascular events and evaluatingcardiovascular health and risk, and further aids the detection ofvascular inflammation in general, local plaque inflammation, and thepresence of unstable coronary lesions. The PVR radiomic signature of theinvention is therefore preferably calculated on the basis of two or moreradiomic features of a PVR and provides a tool for characterising thePVR, for example perivascular tissue such as perivascular adipose tissue(PVAT), for the purpose of assessing cardiovascular or vascular health,predicting the risk of future adverse cardiovascular events in patients,identifying or diagnosing coronary artery disease or coronary heartdisease, and identifying unstable coronary lesions or vascularinflammation, for example as caused by local plaques.

The PVR radiomic signature of the invention may be used on its own tocharacterise the PVR or to provide diagnostic or prognostic information,or it may be combined with existing models, such as the FAI_(PVAT), theDuke Prognostic CAD index and/or other conventional models includingdemographics and risk factors, such as the presence of coronary calcium,high-risk plaque features, and/or EAT (epicardial adipose tissue)volume.

The invention exploits the fact that the coronary wall and the adjacentPVR, in particular tissues within the PVR such as adipose tissue,interact in a bidirectional manner. Vascular-induced phenotypic changesin coronary PVR can therefore function as a sensor of underlyingdisease, even in the absence of visible coronary lesions. In particular,the invention exploits the effect that this interaction has on thetexture (e.g. the spatial non-uniformity or variability) of the PVR, andthe radiomic signature of the invention may therefore be constructed toprovide a measure of the texture of the PVR. The radiomic signature ofthe invention may therefore also be referred to as the perivasculartexture index (PTI). However, the radiomics-based approach used toconstruct the signature of the invention is not specific to constructinga radiomic signature that measures texture and it is the prognosticvalue of the resulting signature that is of primary importance. It istherefore not strictly necessary for the radiomic signature to measuretexture in order to be an effective prognostic or diagnostic tool.

The PVR refers to a region or volume adjacent to a blood vessel. The PVRmay be a region or volume of perivascular tissue (PVT) or may compriseor consist of PVT. Perivascular tissue is tissue located adjacent to ablood vessel. Tissue is a complex biological structure, and may comprisecells (e.g. adipocytes, neurons, etc.) and extracellular structures andmaterials (such as water) which may occupy the intercellular spaces. Inparticular, the PVT may comprise or consist of perivascular adiposetissue (PVAT) and the PVR may therefore alternatively be referred to asa region or volume of PVAT.

The invention exploits a radiomic approach. Radiomics is a field ofimaging in which a large amount of quantitative information is extractedfrom imaging data using data-characterization algorithms. The resultingfeatures, referred to as radiomic features, range from simplevolumetric, shape-related or first order statistics (such as mean ormedian attenuation), to second and higher order statistics that describethe texture of a segmented volume or region and the spatial relationshipof voxels with similar or different attenuation values. Such featurescan identify imaging patterns of significant clinical value that cannotbe recognized by the naked eye and have the potential to maximize thediagnostic yield of non-invasive PVR phenotyping.

The signature of the invention is derived and calculated on the basis ofradiomic features, for example those extracted from medical imagingdata. In particular, the medical imaging data from which the radiomicfeatures are extracted correspond to a perivascular region (PVR), forexample coronary PVR such as coronary perivascular adipose tissue(PVAT), and optionally also to the blood vessel itself and/or othertissue adjacent or surrounding the PVR. The medical imaging datatypically comprise radiodensity (or attenuation) values, usuallyexpressed in Hounsfield Units (HU), for a plurality of voxels of therelevant region, in this case the PVR, and optionally also the adjacenttissues.

The medical imaging data are preferably computed tomography (CT) data,such as coronary computed tomography angiography (CCTA), but other formsof medical imaging data (e.g. radiography data) that provide attenuation(or radiodensity) data for voxels of the imaged region may be usedinstead, such as three-dimensional computed laminography data.Typically, the medical imaging data used in the invention arethree-dimensional imaging data. Throughout the following, where CCTA oranother medical imaging technique is referred to, it should beunderstood that other suitable medical imaging techniques couldalternatively be used.

The PVR may include only voxels having a radiodensity (or attenuation)falling within a given or predetermined range and/or located within adelineated region, for example within a given or predetermined radialdistance from an outer vessel wall. The given radial distance ispreferably a distance related to or dependent on one or more dimensionsof the adjacent vessel, such as its diameter or radius. However, theradial distance may instead be a set or fixed value, such as about 5 mm.Alternatively, the PVR may be identified by manual contouring ordelineation by a human operator, optionally also in combination withapplying a radiodensity or attenuation mask so that only voxels having aradiodensity within a specified range and falling within the delineatedregion are included. For example, the operator may identify the PVRthrough an inspection of the data, for example the CT image. The PVR mayinclude only voxels having a radiodensity in the Hounsfield Unit rangeof about −190 HU to about +30 HU. For example, the PVR may include onlyvoxels having a radiodensity in the Hounsfield Unit range of about −190HU to about −30 HU. This range of attenuation values generallycorresponds to the radiodensity of perivascular adipose tissue (PVAT).However, other ranges could be used, for example about −30 to about +30Hounsfield Units, which generally corresponds to the radiodensity ofwater. In particular, the PVR may be identified as all voxels having aradiodensity in the Hounsfield Unit range of about −190 HU to about −30HU and located within a radial distance from the adjacent outer vesselwall approximately equal to the diameter of the adjacent vessel.

The radiomic features, and therefore also the radiomic signature, may becalculated for a particular blood vessel, for example a coronary vesselsuch as a coronary artery. The proximal and mid right coronary artery(RCA) (segments 1 and 2 according to the anatomical classification ofthe American Heart Association, for example as defined in Austen W G,Edwards J E, Frye R L, et al. A reporting system on patients evaluatedfor coronary artery disease. Report of the Ad Hoc Committee for Gradingof Coronary Artery Disease, Council on Cardiovascular Surgery, AmericanHeart Association. Circulation 1975; 51(4 Suppl): 5-40) is particularlysuitable due to its straight course and absence of large branches. ThePVR may therefore be located adjacent to a particular blood vessel.

The PVR may be segmented prior to calculating the radiomic features andthe radiomic features may be calculated from the segmented data. Thesegmented volume or region corresponds to the PVR, and segmentation mayremove data corresponding to voxels that are outside of the PVR.Segmentation may therefore be achieved by identifying the PVR, asdescribed above, and then removing any voxels from the data that areidentified as not being part of the PVR, for example those voxelscorresponding to surrounding or adjacent tissue voxels. Segmentation maybe performed by placing a three-dimensional sphere with a diameter equalto the diameter of the blood vessel plus twice the given distance fromthe outer vessel wall within which the PVR may be identified onconsecutive slices following the centreline of the vessel. For example,if PVR is identified as being located within a radial distance from theouter vessel wall equal to the diameter of the adjacent vessel then thesphere will have a diameter equal to three times the diameter of theadjacent vessel. The segmented PVR may be extracted and used tocalculate the radiomic features.

Calculation of the radiomic features from the medical imaging data maybe performed using a computer program, or software. Various commerciallyavailable software packages exist for this purpose, such as 3D Slicer.The radiomic features may be shape-related statistics, first-orderstatistics, or texture statistics (e.g. second and higher orderstatistics). Shape-related and first-order radiomic features may becalculated using the raw radiodensity (HU) values of the PVR voxels. Forcalculation of texture features (e.g. Gray Level Co-occurrence Matrix[GLCM], Gray Level Dependence Matrix [GLDM], Gray Level Run-LengthMatrix [GLRLM], Gray Level Size Zone Matrix [GLSZM], and NeighbouringGray Tone Difference Matrix [NGTDM], see FIG. 1A and Tables R1-R7), PVRvoxel radiodensity or attenuation values are preferably discretized intoa plurality of bins, preferably into 16 bins, preferably of equal width(e.g. width of ten HU), to reduce noise while allowing a sufficientresolution to detect biologically significant spatial changes in PVRattenuation. Discretization into 16 bins is recommended as the optimalapproach to increase the signal-to-noise ratio of images for radiomicanalysis. However, discretization into more or fewer than 16 bins isalso possible. To enforce symmetrical, rotationally-invariant results,some or all of the radiomic features, in particular the texturestatistics (GLCM etc), may be calculated in all (orthogonal) directionsand then averaged (e.g. using the mean or other average of theindividually calculated values of the feature in each of the fourdirections).

Some or all of the radiomic features, in particular those relating tofirst order and texture-based statistics, may also be calculated forthree-dimensional wavelet transformations of the original image dataresulting in a number of additional sets of radiomic features (FIG. 1A),for example as described by Guo et al. (Guo X, Liu X, Wang H, et al.Enhanced CT images by the wavelet transform improving diagnosticaccuracy of chest nodules. J Digit Imaging 2011; 24(1): 44-9). Wavelettransformation decomposes the data into high and low frequencycomponents. At high frequency (shorter time intervals), the resultingwavelets can capture discontinuities, ruptures and singularities in theoriginal data. At low frequency (longer time intervals), the waveletscharacterize the coarse structure of the data to identify the long-termtrends. Thus, the wavelet analysis allows extraction of hidden andsignificant temporal features of the original data, while improving thesignal-to-noise ratio of imaging studies. The data may be decomposed bya discrete wavelet transform into a plurality (e.g. eight) waveletdecompositions by passing the data through a multi-level (e.g. threelevel) filter bank. At each level, the data are decomposed into high-and low-frequency components by high- and low-pass filters,respectively. Thus, if a three level filter bank is used, eight waveletdecompositions result, corresponding to HHH, HHL, HLH, HLL, LHH, LHL,LLH and LLL, where H refers to “high-pass”, and L refers to “low-pass”.Of course, more or fewer than eight levels could alternatively be usedto decompose the data. Such decompositions may be performed using widelyavailable software, such as the Slicer Radiomics software package whichincorporates the Pyradiomics library. Where a radiomic feature iscalculated on the basis of a wavelet decomposition or transformation ofthe data this is denoted by a suffix indicating which waveletdecomposition the radiomic feature has been calculated on the basis of(e.g. HHH for high-pass, high-pass, high-pass). So, for example,“Skewness LLL” denotes the radiomic feature “Skewness” as calculated onthe basis of the LLL wavelet decomposition. Where no suffix is present,the radiomic feature is calculated on the basis of the original (or raw)data.

Deriving a Radiomic Signature

The invention provides a method for deriving a radiomic signature forcharacterising a PVR (for example a region of perivascular adiposetissue), for example for predicting cardiovascular risk. The radiomicsignature is derived using medical imaging data for a plurality ofindividuals, and data including the occurrence of clinical endpointevents for each of the plurality of individuals within a subsequentperiod after the medical imaging data were collected. In particular, theclinical endpoint is preferably indicative of cardiovascular health orrisk.

The method typically involves performing a case-control study of (human)patients with versus without adverse (clinical endpoint) events within apredetermined or subsequent time period, preferably five years, afterthe imaging data are collected, for example by clinically-indicatedassessment by CCTA or other medical imaging technique. The individualsreaching the clinical endpoint are the cases (first group) and theindividuals not reaching the clinical endpoint are the controls (secondgroup).

The plurality of individuals (also referred to herein as patients) maybe divided into two independent cohorts of patients undergoing (or whohave undergone) medical imaging, specifically a training cohort and avalidation cohort. Cases are identified based on the occurrence ofclinical endpoint events within a specified or predetermined periodfollowing the collection of the medical imaging data, i.e. thesubsequent period. The subsequent period is preferably at least aboutfive years, preferably about five years, but could be longer or shorter.The clinical endpoint is preferably be the primary composite endpoint ofmajor adverse cardiovascular events (MACE), which may be defined as thecomposite of all-cause mortality and non-fatal myocardial infarction(MI) within the specified period (preferably five years) following thecollection of the medical imaging data, or the primary compositeendpoint of cardiac-specific MACE (cMACE, i.e. cardiac mortality andnon-fatal MI) within the specified period (preferably five years)following the collection of the medical imaging data.

Cardiac and non-cardiac mortality, as used herein, may be definedaccording to the recommendations of the ACC/AHA (Hicks K A, Tcheng J E,Bozkurt B, et al. 2014 ACC/AHA Key Data Elements and Definitions forCardiovascular Endpoint Events in Clinical Trials: A Report of theAmerican College of Cardiology/American Heart Association Task Force onClinical Data Standards (Writing Committee to Develop CardiovascularEndpoints Data Standards). J Am Coll Cardiol 2015; 66(4): 403-69). Morespecifically, cardiac mortality may be defined as any death due toproximate cardiac causes (e.g. myocardial infarction, low-output heartfailure, fatal arrhythmia). Deaths fulfilling the criteria of suddencardiac death may also be included in this group. Any death not coveredby the previous definition, such as death caused by malignancy,accident, infection, sepsis, renal failure, suicide or other non-cardiacvascular causes such as stroke or pulmonary embolism may be classifiedas non-cardiac.

Controls are preferably identified as patients with event-free follow-upwithin the same specified period, for example for at least five yearspost-CCTA. 1:1 case-control matching is preferably performed to matchcases with controls, for example using an automated algorithm. The casesand controls may be matched for clinical demographics (such as age, sex,obesity status), cohort and/or technical parameters related to imagingdata acquisition (e.g. tube voltage and CT scanner used). Preferably,patients are also matched for other cardiovascular risk factors,including hypertension, dyslipidemia, diabetes mellitus and smoking.

Hypertension may be defined based on the presence of a documenteddiagnosis or treatment with an antihypertensive regimen, according tothe relevant clinical guidelines (James P A, Oparil S, Carter B L, etal. 2014 evidence-based guideline for the management of high bloodpressure in adults: report from the panel members appointed to theEighth Joint National Committee (JNC 8). JAMA 2014; 311(5): 507-20).Similar criteria may be applied for the definition ofhypercholesterolemia and diabetes mellitus (American Diabetes A.Diagnosis and classification of diabetes mellitus. Diabetes Care 2014;37 Suppl 1: S81-90; Stone N J, Robinson J G, Lichtenstein A H, et al.2013 ACC/AHA guideline on the treatment of blood cholesterol to reduceatherosclerotic cardiovascular risk in adults: a report of the AmericanCollege of Cardiology/American Heart Association Task Force on PracticeGuidelines. J Am Coll Cardiol 2014; 63(25 Pt B): 2889-934).

“Clustering” (or Collinear Elimination) Method

A stepwise approach may then be followed to develop a radiomicsignature, as schematically illustrated in FIG. 2. First, a plurality ofradiomic features are calculated from the medical imaging data for eachof the plurality of individuals, for example as described above. Theradiomic features may comprise a selection or all of the radiomicfeatures as defined in Tables R1-R7, and each of the radiomic featuresmay be calculated based on the raw image data and/or on one or morewavelet transformations of the image data (or wavelet decompositions),as described above. Preferably, each of the radiomic features iscalculated for the raw image data and for the aforementioned eightthree-dimensional wavelet decompositions of the image data.

Unstable features may be removed from the plurality of radiomicfeatures. A z-score transformation may be applied to the features (i.e.expressing the values of the radiomic features in terms of the number ofstandard deviations from the mean) and the stability analysis performedon the basis of the z-scores. Unstable radiomic features are identifiedas those having an intraclass correlation coefficient (ICC) in repeatimaging data acquisitions (e.g. imaging scans) below a stabilitythreshold. For example, the stability threshold may be at least about0.9, for example about 0.9, so that all radiomic features having anICC<0.9 are excluded (FIG. 3). However, other stability thresholds maybe used instead, such as 0.85 or 0.95. The ICC may be calculated for aplurality of repeat scans, for example two to ten scans, in particulartwo or ten scans. In other words, a stability analysis may be performedon the PVR radiomic features and unstable radiomic features removed fromthe plurality of radiomic features. The stability analysis may beperformed on the basis of the imaging data for the plurality ofindividuals, or may be performed using other data, for example referencedata such as the RIDER dataset (The Reference Image Database to EvaluateTherapy Response).

Preferably, if the plurality of radiomic features includes any volume-and orientation-dependent radiomic features these are then excluded(i.e. removed from the plurality of radiomic features). Alternatively,any volume- and orientation-dependent features may be excluded from thestart so that such a step is not necessary. In other words, the initialplurality of radiomic features may each be volume- andorientation-independent. Volume dependent features may include Energyand Total Energy (original and wavelet calculated), andorientation-dependent features may include those derived from thewavelet transformations HLL, HLH, LLH, HLL, LHL, LHH (i.e. all but LLLor HHH, or those wavelet transformations that are not exclusively high-or low-pass).

Radiomic features that are not significantly associated (e.g.correlated) with the clinical endpoint, for example 5-year MACE orcMACE, above a significance threshold may then be removed from theplurality of radiomic features. The association of each radiomic featurewith the clinical endpoint may be calculated on the basis of a receiveroperating characteristic curve (ROC) analysis, in particular an areaunder the curve calculation, based on the data for the plurality ofindividuals. The significance threshold is preferably α=0.05 or lower,for example a may be in the range of from 0.001 to 0.05. Thesignificance threshold is preferably about α=0.05. However, thesignificance threshold may be about α=0.04. Alternatively, thesignificance threshold may be about α=0.03. Alternatively, thesignificance threshold may be about α=0.02. Alternatively, thesignificance threshold may be about α=0.01. Alternatively, thesignificance threshold may be about α=0.005. Alternatively, thesignificance threshold may be about α=0.002. Preferably, the radiomicfeatures must be identified as being significantly associated with theclinical endpoint in both the training and validation cohorts in orderto be retained, and any that are found to be not significantlyassociated with the clinical endpoint in one or both cohorts are removedin order to reduce positive findings due to cohort-specific variations.However, radiomic features that are found to be significantly associatedwith the clinical endpoint in only one of the cohorts, for example thetraining cohort, may instead be retained. Alternatively, the assessmentof whether each of the radiomic features is significantly associatedwith the clinical endpoint may be performed on the basis of pooled datafor both cohorts, i.e. for all of the plurality of individuals. In otherwords, the method may involve evaluating the significance of theradiomic features with the clinical endpoint and removing features thatare found to be not significantly associated with the clinical endpointfrom the plurality of features. The end result should be that anyradiomic features that are not significantly associated with theclinical endpoint (as determined or calculated from the data, forexample based on an analysis of the data) are removed from the pluralityof radiomic features.

Collinearity of the retained radiomic features (i.e. those that aresignificantly associated with the clinical endpoint, otherwise known assignificant radiomic features) may then be reduced or eliminated byremoving pairwise correlations, i.e. by removing at least one of eachpair of collinear radiomic features. The correlation between theradiomic features are generally calculated using the measured values ofthe radiomic features for the plurality of individuals. The removal ofpairwise correlations may be performed in a stepwise manner. Collinearradiomic features may be identified as those that are correlated witheach other to a degree at least equal to a given correlation threshold.The correlation threshold preferably applies to both positive andnegative correlations, for example the correlation threshold may beexpressed as a modulus. The pairwise correlations may be calculatedusing Spearman's rho coefficient and the correlation threshold may be atleast about |rho|=0.75, for example about |rho|=0.75, so that allpairwise correlations at the level of |rho|≥0.75 are eliminated. As willbe readily understood in the field, the correlation or collinearity is ameasure of how closely two radiomic features vary together from oneindividual to the next and may be calculated on the basis of themeasured radiomic feature values for the plurality of individuals.

For example, when a pair of collinear radiomic features is identified,one of the two features is preferably eliminated from the plurality offeatures. For example, the radiomic feature that is calculated from thedata to be the less strongly associated with the clinical endpoint ofthe two may be eliminated and the radiomic feature that is most stronglyassociated with the clinical endpoint may be retained, but this is notnecessary and either could be retained or eliminated. For example, thecollinear elimination step may be performed in an unsupervised waywithout taking into account the clinical endpoint and the algorithm mayeliminate the most redundant feature that contributes the least to thevariation of the study population (e.g. the feature with the smallervariance as measured across the plurality of individuals). In oneexample, when a pair of collinear features is identified, the featurewith the largest average (e.g. mean) absolute correlation (i.e. theaverage correlation value (or average modulus or square correlationvalue) with all other radiomic features) is removed. This may beperformed in a stepwise manner until no collinear radiomic featuresremain.

The collinear elimination step may be performed using an algorithm orfunction, (for example, the function claret::findCorrelation, R package,see Kuhn, M. & Johnson, K. Applied Predictive Modelling. (Springer,2013)). For example, the function or algorithm may construct a pairwisecorrelation matrix containing pairwise correlations between the radiomicfeatures. The function may then search through the correlation matrixand return a vector of integers corresponding to columns to remove toreduce pairwise correlations. The radiomic features to which thesecolumns correspond may then be removed from the plurality of radiomicfeatures. In deciding which columns to remove, the algorithm may firstidentify pairwise correlations between radiomic features. When twocollinear radiomic features are identified, the algorithm thenidentifies the column corresponding to the feature with the largest meanabsolute correlation for removal.

Regardless of how the collinear elimination step is performed, the endresult is preferably the production of a reduced plurality of radiomicfeatures in which each of the features is correlated with each of theother remaining features to a degree less than the correlationthreshold. In other words, the method may involve the step of removingradiomic features to eliminate collinearity between the radiomicfeatures so that none of the remaining radiomic features is collinearwith any of the other remaining radiomic features. This may involve thecalculation of pairwise correlations between radiomic features andremoving at least one of any identified pair of collinear features.

The radiomic signature may then be constructed based on at least two ofthe remaining radiomic features that survive whichever of the stepsdescribed above are performed (e.g. stability analysis, significanceanalysis and/or collinearity elimination). For example the radiomicsignature may then be constructed based on at least two of the reducedplurality of non-collinear radiomic features that survive the collinearelimination step. The reduced plurality of features that survive thecollinear elimination step are otherwise known as the “originalfeatures”. However, since the eliminated radiomic features are eachstrongly correlated with at least one of the original features, asignature in which one or more of the original features is replaced byone of the features that is collinear with the replaced original featurewill generally perform similarly to a signature calculated on the basisof only the original features. For example, it is possible to swap oneof the original features for one of the features calculated as beingcollinear with that original feature and the signature should performsimilarly. In fact, it is possible that replacing one or more (or evenall) of the original features with alternative features that arecollinear with the replaced original features could result in asignature having an enhanced prognostic value, and this has in fact beenfound to be the case in some instances (see, for example, Tables 8A and8B). This is because although the original features are generally themost independently associated with the clinical endpoint, they are notnecessarily the best-performing features when combined into a signature.

The process of constructing the radiomic signature may therefore involvethe construction of “clusters” of radiomic features (each clustercomprising one of the original features) in which each of the radiomicfeatures in each cluster is collinear with at least the “original”feature in that cluster (i.e. the feature of that cluster that survivedthe collinear elimination step, e.g. the feature in the cluster moststrongly independently associated with the clinical endpoint). Theconstruction of these clusters may be performed instead of the collinearelimination step. For example, instead of eliminating one of each pairof collinear features, the collinear features may be allocated to thesame cluster. Alternatively, the pairwise elimination step may beperformed as described above, and then, once the original features areidentified, the eliminated features may be reintroduced by allocatingthem to the cluster of the original feature with which they are moststrongly correlated or collinear with.

However, regardless of how the clusters are constructed, the end resultshould be that each radiomic feature is allocated to the same cluster asthe original radiomic feature(s) that it is collinear with. If aradiomic feature is collinear with two “original” features, it ispreferably allocated to the cluster of the original feature with whichit is most collinear with, but it may be allocated to the clusters ofall the original features with which it is collinear.

The clusters may also be expanded to include any of the originalplurality of radiomic features that are collinear with the “original”radiomic feature of that cluster, regardless of whether the radiomicfeatures are themselves independently significantly associated with theclinical endpoint. However, preferably any radiomic features included inthe clusters are stable, as previously mentioned.

The “original” radiomic feature in each cluster therefore represents a“partner” radiomic features to each of the other radiomic features inthat cluster, with each of the radiomic features in each cluster beingcollinear with its “partner” feature. The original radiomic feature maytherefore be considered its own “partner” radiomic feature in this sensebecause it is perfectly collinear with itself.

An initial radiomic signature may then be constructed based on at leasttwo (or all) of the reduced plurality of features (e.g. the “original”features). Alternatively, if clusters are constructed, the initialradiomic signature may be constructed from at least two radiomicfeatures, each being selected from a different cluster. The constructionof the radiomic signature involves refining or optimising the radiomicsignature, in particular using data for the “training” cohort. Thisinvolves refining or optimising the contribution of each of each of theremaining radiomic features to the signature to improve the correlationor association of the signature with the clinical endpoint based on thedata. For example, the signature may comprise a weighted sum of thevalues of each of the radiomic features included in the initialsignature, and the weighing of each of the radiomic features may beprogressively optimised or refined. The coefficients by which each ofthe radiomic features is multiplied are generally referred to as beta(β) coefficients, and it is these beta coefficients that may beoptimised or refined.

Preferably all of the reduced plurality of features are included in theinitial radiomic signature to be refined, e.g. one feature from eachcluster, but this is not absolutely necessary. For example, the “top” or“original” feature from each cluster may be included (e.g. the featuremost strongly independently associated with the clinical endpoint).Other radiomic features may also be included in the initial signature tobe optimised, for example two or more radiomic features from any or allof the clusters may be included in the initial signature. However, inorder to provide a signature more strongly associated with the clinicalendpoint, and therefore of enhanced diagnostic and prognosticusefulness, it is preferable to include at least two radiomic features,each from a different cluster. This is because features from differentclusters provide complementary information relating to the PVR. Inparticular, radiomic features from different clusters will be sensitiveto different phenotypic characteristics of the PVR because they arecollinear with different “original” or “partner” features. For example,the initial radiomic signature may comprise at least three radiomicfeatures, each selected from a different cluster. Alternatively, theinitial radiomic signature may comprise at least four radiomic features,each selected from a different cluster. Alternatively, the initialradiomic signature may comprise at least five radiomic features, eachselected from a different cluster. Alternatively, the initial radiomicsignature may comprise at least six radiomic features, each selectedfrom a different cluster. Alternatively, the initial radiomic signaturemay comprise at least seven radiomic features, each selected from adifferent cluster. Alternatively, the initial radiomic signature maycomprise at least eight radiomic features, each selected from adifferent cluster. Preferably, the initial radiomic signature maycomprise one radiomic feature from each cluster.

Once the initial radiomic signature has been refined, the final radiomicsignature may then be constructed based on all of the radiomic featuresincluded in the initial signature, or on a subset of those features. Forexample, the optimised or refined initial signature may be used as thefinal signature. Alternatively, the final radiomic signature maycomprise only a subset of the radiomic features included in the initialsignature. For example, only those parameters having a contribution tothe refined initial signature above a certain threshold may be includedin the final signature, such as those having an optimised weightingcoefficient (e.g. beta parameter) above a certain (e.g. predetermined)threshold. In other words, those radiomic features that have optimisedcoefficients below a given threshold are removed from the finalsignature. For example, the top seven features (i.e. those with thelargest contribution to the refined signature) may be included in thefinal signature.

If only a subset of the radiomic features is included in the finalsignature, one option is to re-optimise or refine the signature basedonly on the subset of features. For example, the coefficients or betaparameters may be re-optimised for the subset of radiomic featuresincluded in the final signature. Alternatively, the coefficients or betaparameters derived from the initial optimisation performed on theinitial signature can be used in the final signature.

As mentioned above, the signature may include a weighted sum of thecalculated values of a plurality of radiomic features. The signature mayalso include other terms, such as the addition or subtraction of aconstant, or multiplication by a factor. However, typically thesignature will be linearly related to the weighted sum of radiomicfeature values in some way.

The radiomic signature may take the form of, or include the term (forexample, the signature may be calculated on the basis of a functionincluding the term):

A±Σb _(i) rf _(i)

where A is a constant (which can be zero or non-zero), b_(i) is theweighting coefficient (or beta patameter) for the radiomic feature i,and rf_(i) is the measured value of the radiomic feature i. The betaparameter in the equation is preferably the unstandardized beta, whichis the Z-score beta parameter multiplied by the standard deviation ofthe radiomic feature, where the standard deviation is preferably thestandard deviation of the radiomic feature in the training or derivationcohort. The constant A is not necessary but may be included to ensurethat all resulting values are either positive or negative, preferablypositive. Preferably the “±” is a “−”.

The initial and/or final radiomic signature may be constructed (i.e.optimised or refined) using a machine learning algorithm. For example,the machine learning algorithm may be used to refine or optimise thecontribution of each of the radiomic features to the signature, forexample by optimising the beta coefficients. The machine learningapproach may use elastic net/lasso regression and may utiliseleave-one-out internal cross-validation. Elastic net regression is aregularized regression method that linearly combines the L1 and L2penalties of the lasso and ridge methods. L1 (least absolute shrinkageand selection operator “LASSO” penalty) penalizes the absolute values ofthe coefficients, shrinking irrelevant coefficients to zero andcontributing to feature selection, whereas L2 (“ridge” penalty)penalizes the squares of the coefficients, therefore limiting the impactof collinearity and reducing overfitting. The optimal penaltycoefficient (lambda, may be selected by cross-validation, while alpha ispreferably set at α=1.

Preferably, the signature is refined using data for the training cohort,and is then validated externally using data for the training cohort.

“Non-Clustering” Method

The invention also provides another method for deriving a radiomicsignature. In this method, a plurality of radiomic features arecalculated from the medical imaging data for each of the plurality ofindividuals, as described above in relation to the “clustering” method.

The discriminatory value of all radiomic features (preferably all stableradiomic features) for the clinical endpoint, for example 5-year MACE,may then be evaluated, for example using receiver operatingcharacteristic curve (ROC) analysis, in particular using an area underthe curve calculation (calculating the C-statistics), and any radiomicfeatures that are not significantly associated with the clinicalendpoint are eliminated from the plurality of features. As for theclustering method described above, features are identified as beingsignificantly associated with the clinical endpoint if they areassociated with the clinical endpoint above a certain significancethreshold. The significance threshold is preferably α=0.05 or lower, forexample α=0.001 to 0.05. The significance threshold is preferably aboutα=0.05. However, the significance threshold may be about α=0.04.Alternatively, the significance threshold may be about α=0.03.Alternatively, the significance threshold may be about α=0.02.Alternatively, the significance threshold may be about α=0.01.Alternatively, the significance threshold may be about α=0.005.Alternatively, the significance threshold may be about α=0.002.

To correct for multiple comparisons and to decrease the false discoveryrate (FDR), a Bonferroni correction may be applied to the significancethreshold. The Bonferroni correction may be applied based on the numberof principal components which account for a given amount of variabilityin the study sample based on a principal component analysis. Forexample, the given amount may be about 99.5%. In other words the m valueused to correct the a value (by dividing a by m, i.e. a/m) is the numberof principal components that account for the given amount ofvariability. For this reason, a principal component analysis of theradiomic features may be performed on the data for the plurality ofindividuals (preferably including both cohorts, if the individuals aredivided into training and validation cohorts).

The radiomic signature may then be constructed based on at least two ofthe remaining radiomic features, i.e. those that are identified as beingsignificantly associated with the clinical endpoint, as described above.The radiomic signature may be constructed and optimised in the same wayas described for the clustering method above, but with the differencethat there is no requirement to select radiomic features from differentclusters.

For example, all of the radiomic features identified as significantlyassociated with the clinical endpoint may be included in the initial orfinal radiomic signature. Alternatively, only a subset of the radiomicfeatures significantly associated with the clinical endpoint may beincluded in the initial or final signature, for example at least two.Alternatively, at least three of the radiomic features significantlyassociated with the clinical endpoint may be included in the initial orfinal signature. Alternatively, at least four of the radiomic featuressignificantly associated with the clinical endpoint may be included inthe initial or final signature. Alternatively, at least five of theradiomic features significantly associated with the clinical endpointmay be included in the initial or final signature. Alternatively, atleast six of the radiomic features significantly associated with theclinical endpoint may be included in the initial or final signature.Alternatively, at least seven of the radiomic features significantlyassociated with the clinical endpoint may be included in the initial orfinal signature.

Again, the signature is preferably refined using data for the trainingcohort, and is then validated externally using data for the trainingcohort.

Elements of either the clustering or the non-clustering methods may becombined. For example, the clustering (or collinear elimination) methodmay involve the application of a Bonferroni correction.

For example, the plurality of radiomic features may be input into themachine learning algorithm without performing some (or any) of thepreceding steps described above. Usually, however, at least the step ofeliminating unstable radiomic features will be performed before thefeatures are input into the machine learning algorithm.

In general, in the above-described methods (both clustering andnon-clustering), bivariate associations between radiomic features may beassessed by the non-parametric Spearman's rho (ρ) coefficient, whereasintra-observer variability may be assessed in a given number of scans,for example at least two scans, for example ten scans, by means of theintraclass correlation coefficient (ICC).

The Radiomic Signature

The PVR radiomic signature of the invention is calculated on the basisof measured values of radiomic features obtained from medical imagingdata. In particular, the PVR radiomic signature is preferably calculatedon the basis of at least two radiomic features.

To improve the prognostic and diagnostic value of the signature, thesignature is preferably calculated on the basis of at least two radiomicfeatures selected from different “clusters” of collinear features, asdescribed above. This reduces redundancy and improves the diversity ofinformation included in the calculation of the signature because thefeatures from different clusters relate to different textural aspects ofthe PVR.

Nine clusters have been identified using the “clustering” method, whichcorrespond to the nine “original” or “partner” features of the reducedplurality of radiomic features that survived the collinear eliminationprocess in the study described in the following “Examples” section. Themembers of the nine clusters are identified in Table 1.

Table 1 also identifies the “original feature”, which is the feature ineach cluster that survives the elimination of collinear features in the“clustering” method described above. The collinearity of the otherfeatures in each cluster with the original feature is expressed in termsof the Ipl coefficient (where p is the non-parametric Spearman's rho (ρ)coefficient).

To construct the clusters of Table 1, the 53 stable volume- andorientation-independent radiomic features that were associated with theclinical endpoint above the threshold value (p<0.05; where p is theprobability value or asymptotic significance, i.e. α=0.05) in both thetraining and validation cohorts were clustered based on the strength oftheir correlation with the original features. If a radiomic feature wasfound to be collinear with two or more original features (|rho|≥0.75)then it was assigned to the cluster of the original feature with whichit was most strongly associated. Interestingly, and perhapssurprisingly, FAI_(PVAT) was not associated with any of the originalfeatures at a level of |rho|≥0.75 and is therefore not included in anyof the clusters. This demonstrates that the present invention provides aseparate and distinct prognostic and diagnostic tool as compared tocalculating the FAI_(PVAT) and is therefore complementary to theFAI_(PVAT).

TABLE 1 Radiomic features of “standard” clusters selected from amongstthe 53 identified features significantly associated with MACE Clustersand associated features |rho| with original feature Cluster #1: Originalfeature: Short Run High Gray Level Emphasis (SRHGLE) High Gray LevelEmphasis 0.975139 High Gray Level Run Emphasis 0.970598 Cluster #2:Original feature: Skewness Skewness LLL 0.962394 Kurtosis 0.87167590^(th) Percentile 0.851577 Median LLL 0.817939 Kurtosis LLL 0.809719Median 0.789633 Cluster #3: Original feature: Run Entropy Run EntropyLLL 0.79152 Mean LLL 0.771156 Cluster #4: Original feature: Small AreaLow Gray Level Emphasis (SALGLE) Low Gray Level Zone Emphasis 0.970552Gray Level Variance (GLSZM) 0.763504 Cluster #5: Original feature: ZoneEntropy Gray Level Non Uniformity Normalized (GLRLM) 0.891542 Uniformity0.748464 Cluster #6: Original feature: Zone Entropy HHH Cluster #7:Original feature: Strength Cluster #8: Original feature: ClusterTendency LLL Cluster Tendency 0.993906 Mean Absolute Deviation LLL0.974087 Gray Level Variance LLL (GLDM) 0.972331 Variance LLL 0.972329Gray Level Variance LLL (GLRLM) 0.972277 Robust Mean Absolute DeviationLLL 0.961639 Gray Level Variance LLL (GLSZM) 0.957704 InterquartileRange LLL 0.954142 Sum Entropy LLL 0.951601 Gray Level Variance (GLRLM)0.951422 Variance 0.950236 Gray Level Variance (GLDM) 0.950177 MeanAbsolute Deviation 0.945289 Sum Entropy 0.929493 Robust Mean AbsoluteDeviation 0.927285 Interquartile Range 0.920743 Entropy LLL 0.91902210^(th) Percentile LLL 0.911394 10^(th) Percentile 0.898283 Entropy0.860123 Uniformity LLL 0.852958 Gray Level Non Uniformity NormalizedLLL (GLDM) 0.852183 Gray Level Non Uniformity Normalized LLL (GLRLM)0.827855 Root Mean Squared 0.801892 Gray Level Non Uniformity Normalized(GLDM) 0.789831 Root Mean Squared LLL 0.783096 Long Run Low Gray LevelEmphasis 0.775822 Cluster #9: Original feature: Size Zone Non UniformityLLL (SZNU LLL) Busyness 0.879348 Size Zone Non Uniformity 0.856038

As mentioned previously, the clusters may be expanded to include stablemembers of the original plurality of radiomic features that arecollinear with the “original” radiomic features of the clusters,regardless of whether the collinear radiomic features are themselvesindependently significantly associated with the clinical endpoint.

The members of the nine “expanded” clusters are presented in Table 2.These expanded clusters are equivalent to the original clusterspresented in Table 1, but expanded to include any of the 719 stableradiomic features (ICC>0.9) that are also collinear with one of theoriginal features from each cluster (|rho|≥0.75). Again, if a radiomicfeature was found to be collinear with two or more original features(|rho|≥0.75) then it was assigned to the cluster of the original featurewith which it was found to be most strongly associated.

TABLE 2 Radiomic features of “expanded” clusters selected from amongstthe 719 identified stable features Clusters and associated features|rho| with original feature Cluster #1: Original feature: Short Run HighGray Level Emphasis (SRHGLE) High Gray Level Emphasis 0.975139 High GrayLevel Run Emphasis 0.970598 Autocorrelation 0.935379 Sum Average0.891625 Joint Average 0.891625 High Gray Level Zone Emphasis 0.757022Cluster #2: Original feature: Skewness Skewness LLL 0.962394 Kurtosis0.871675 90^(th) Percentile 0.851577 90^(th) Percentile LLL 0.838578Median LLL 0.817939 Kurtosis LLL 0.809719 Median 0.789633 Cluster #3:Original feature: Run Entropy Dependence Entropy LLL 0.905264 DependenceEntropy 0.850414 Zone Entropy LLL 0.837804 Run Entropy LLL 0.79152 MeanLLL 0.771156 Cluster #4: Original feature: Small Area Low Gray LevelEmphasis (SALGLE) Low Gray Level Zone Emphasis 0.970552 Short Run LowGray Level Emphasis 0.886019 Low Gray Level Run Emphasis 0.877065 LowGray Level Emphasis 0.869863 Small Dependence Low Gray Level Emphasis0.865228 Gray Level Variance LLL (GLSZM) 0.830268 Gray Level Variance(GLDM) 0.806681 Variance 0.802258 Gray Level Variance (GLDM) 0.80188Difference Variance LLL 0.800522 Gray Level Variance LLL (GLRLM )0.791822 Variance LLL 0.789145 Gray Level Variance LLL (GLDM) 0.789125Sum of Squares 0.782797 Contrast LLL 0.775718 Mean Absolute Deviation0.775093 Interquartile Range 0.771971 Robust Mean Absolute Deviation0.770797 Long Run Low Gray Level Emphasis 0.766293 Difference Variance0.766248 Gray Level Variance (GLSZM) 0.763504 Inverse Difference MomentNormalized 0.757157 Mean Absolute Deviation LLL 0.756059 Sum of SquaresLLL 0.75198 Contrast 0.750381 Cluster #5: Original feature: Zone EntropyGray Level Non Uniformity Normalized (GLRLM) 0.891542 Gray Level NonUniformity Normalized LLL (GLRLM) 0.81717 Sum Entropy 0.776994 JointEnergy 0.775664 Entropy 0.774753 Gray Level Non Uniformity Normalized(GLDM) 0.767903 Joint Energy LLL 0.764334 Gray Level Non UniformityNormalized LLL (GLDM) 0.762338 Uniformity LLL 0.759166 Sum Entropy LLL0.754785 Uniformity 0.748464 Cluster #6: Original feature: Zone EntropyHHH Size Zone Non Uniformity Normalized HHH 0.814641 Small Area EmphasisHHH 0.789525 Cluster #7: Original feature: Strength Coarseness HLL0.88454 Coarseness 0.870477 Coarseness LHL 0.86241 Coarseness LLL0.859987 Coarseness LLH 0.855166 Coarseness HHH 0.837053 Coarseness HLH0.791609 Coarseness HHL 0.786734 Coarseness LHH 0.782421 Cluster #8:Original feature: Cluster Tendency LLL Cluster Tendency 0.993906SumSquares LLL 0.98664 Mean Absolute Deviation LLL 0.983493 Gray LevelVariance LLL (GLDM) 0.977069 Variance LLL 0.977064 Gray Level VarianceLLL (GLRLM) 0.976888 Gray Level Variance (GLRLM) 0.971257 Robust MeanAbsolute Deviation LLL 0.971198 Gray Level Variance (GLDM) 0.970257Variance 0.970197 Mean Absolute Deviation 0.968679 Cluster Prominence0.96516 Sum Entropy LLL 0.964505 Interquartile Range LLL 0.964208 GrayLevel Variance LLL (GLSZM) 0.960755 Sum of Squares 0.960157 Robust MeanAbsolute Deviation 0.951646 Sum Entropy 0.950703 Interquartile Range0.945747 Cluster Prominence LLL 0.945739 Entropy LLL 0.943076 10^(th)Percentile LLL 0.931818 10^(th) Percentile 0.928162 Cluster #9: Originalfeature: Size Zone Non Uniformity LLL (SZNU LLL) Dependence NonUniformity HLL 0.928379 Gray Level Non Uniformity HLL (GLSZM) 0.923214Gray Level Non Uniformity (GLSZM) 0.909737 Run Length Non Uniformity HHL0.908087 Run Length Non Uniformity LHL 0.900784 Dependence NonUniformity LHL 0.887204 Dependence Non Uniformity 0.885575 Run LengthNon Uniformity HLH 0.882877 Busyness 0.879348 Run Length Non UniformityLLH 0.875944 Dependence Non Uniformity LLH 0.872262 Dependence NonUniformity LLL 0.867809 Size Zone Non Uniformity 0.856038 Energy HLL0.838125 Run Length Non Uniformity LHH 0.831353 Size Zone Non UniformityHLL 0.809159 Gray Level Non Uniformity LLH (GLSZM) 0.803344 Gray LevelNon Uniformity LHL (GLSZM) 0.801205 Gray Level Non Uniformity LLL(GLSZM) 0.791236 Run Length Non Uniformity HLL 0.786947 Gray Level NonUniformity HLH (GLSZM) 0.778574 Gray Level Non Uniformity HHL (GLSZM)0.778439 Run Length Non Uniformity 0.776126 Run Length Non UniformityHHH 0.751445

The radiomic signature may be constructed from any of the radiomicfeatures included in Table 1 or Table 2 (i.e. the standard or expandedclusters), provided the radiomic signature comprises at least tworadiomic features each selected from different clusters. For example,the radiomic signature may comprise at least three radiomic featuresfrom different clusters. For example, the radiomic signature maycomprise at least four radiomic features from different clusters. Forexample, the radiomic signature may comprise at least five radiomicfeatures from different clusters. For example, the radiomic signaturemay comprise at least six radiomic features from different clusters. Forexample, the radiomic signature may comprise at least seven radiomicfeatures from different clusters. For example, the radiomic signaturemay comprise at least eight radiomic features from different clusters.For example, the radiomic signature may comprise at least nine radiomicfeatures from different clusters.

Each of the at least two (or more) radiomic features that are selectedfrom different clusters may be selected to be correlated with the“original” feature of the clusters to which it belongs to a degree of atleast |rho|=0.8. For example, each of the at least two radiomic featuresfrom different clusters may be correlated with the “original” feature ofthe clusters to which it belongs to a degree of at least |rho|=0.85. Forexample, each of the at least two radiomic features from differentclusters may be correlated with the “original” feature of the clustersto which it belongs to a degree of at least |rho|=0.9. For example, eachof the at least two radiomic features from different clusters may becorrelated with the “original” feature of the clusters to which itbelongs to a degree of at least |rho|=0.95.

In addition to the radiomic signature being calculated on the basis ofat least two radiomic features from different cluster, it may also becalculated on the basis of additional radiomic features. For example,the radiomic signature may include more than one radiomic feature fromany given cluster, or may include radiomic features not included in anyof the clusters.

Alternatively, the radiomic signature may be calculated on the basis ofat least two of the radiomic features that have been found to beindependently associated with the clinical endpoint using the“non-clustering” approach. Thus, the radiomic signature may instead becalculated on the basis of at least two radiomic features selected fromTable 3.

TABLE 3 Radiomic features identified as significantly associated withMACE following the “non-clustering” approach Radiomic feature ClassTransformation Bonferroni adj. P value Median_LLL First order LLL 0.0002Mean_LLL First order LLL 0.0003 Median First order Original 0.0003 RootMean Squared_LLL First order LLL 0.0005 Mean First order Original 0.0007Kurtosis First order Original 0.0008 Root Mean Squared First orderOriginal 0.0014 Run Entropy_LLL GLRLM LLL 0.0015 Uniformity First orderOriginal 0.0018 90^(th) Percentile First order Original 0.0020 GrayLevel Non-Uniformity Normalized GLRLM Original 0.0029 Uniformity_LLLFirst order LLL 0.0037 Skewness First order Original 0.0041 Gray LevelNon-Uniformity Normalized_LLL GLRLM LLL 0.0041 10^(th) Percentile_LLLFirst order LLL 0.0042 Skewness_LLL First order LLL 0.0045 10^(th)Percentile First order Original 0.0060 Entropy First order Original0.0070 Interquartile Range_LLL First order LLL 0.0081 Robust MeanAbsolute Deviation_LLL First order LLL 0.0106 Run Entropy GLRLM Original0.0119 Interquartile Range First order Original 0.0138 Sum Entropy GLCMOriginal 0.0139 Gray Level Non-Uniformity Normalized_LLL GLRLM LLL0.0141 Dependence Non-Uniformity_LHL GLDM LHL 0.0152 Kurtosis_LLL Firstorder LLL 0.0153 Run Length Non-Uniformity_HHL GLRLM HHL 0.0156Entropy_LLL First order LLL 0.0161 Robust Mean Absolute Deviation Firstorder Original 0.0201 Sum Entropy_LLL GLCM LLL 0.0223 90^(th)Percentile_LLL First order LLL 0.0267 Run Entropy_HHL GLRLM HHL 0.0297Energy First order Original 0.0312 Energy_LLL First order LLL 0.0328Strength NGTDM Original 0.0337 Autocorrelation GLCM Original 0.0338 MeanAbsolute Deviation_LLL First order LLL 0.0339 High Gray Level EmphasisGLDM Original 0.0344 Joint Average GLCM Original 0.0374 Sum Average GLCMOriginal 0.0374 Short Run High Gray Level Emphasis GLRLM Original 0.0383Energy_HHH First order HHH 0.0384 High Gray Level Run Emphasis GLRLMOriginal 0.0420 Run Entropy_HHH GLRLM HHH 0.0441 Energy_HHL First orderHHL 0.0483 Mean Absolute Deviation First order Original 0.0497

The radiomic signature may be calculated on the basis of at least tworadiomic features from Table 3. For example, the radiomic signature maybe calculated on the basis of at least three radiomic features fromTable 3. For example, the radiomic signature may be calculated on thebasis of at least four radiomic features from Table 3. For example, theradiomic signature may be calculated on the basis of at least fiveradiomic features from Table 3. For example, the radiomic signature maybe calculated on the basis of at least six radiomic features from Table3. For example, the radiomic signature may be calculated on the basis ofat least seven radiomic features from Table 3.

The at least two (or more) radiomic features may be selected from thoseradiomic features in Table 3 that have a Bonferroni adjusted P value of<0.04. For example, those with a Bonferroni adjusted P value of <0.03.For example, those with a Bonferroni adjusted P value of <0.02. Forexample, those with a Bonferroni adjusted P value of <0.01. For example,those with a Bonferroni adjusted P value of <0.005. For example, thosewith a Bonferroni adjusted P value of <0.002.

The signature may be constructed from the radiomic features listed inTable 3, but excluding Mean.

Again, in addition to the radiomic signature being calculated on thebasis of at least two radiomic features selected from those presented inTable 3, it may also be calculated on the basis of additional radiomicfeatures. For example, the radiomic signature may include radiomicfeatures not included in Table 3.

Each of the radiomic signatures of the invention provides astraightforward means for characterising a PVR using medical imagingdata. Because each of the radiomic signatures of the invention is basedon a relatively small number of the total overall number of possibleradiomic features that can be measured, the signature is simple tocalculate and understand, and its physiological significance can bebetter appreciated by the clinician.

System

The methods of the invention may be performed on a system, such as acomputer system. The invention therefore also provides a system that isconfigured or arranged to perform one or more of the methods of theinvention. For example, the system may comprise a computer processorconfigured to perform one or more of the methods, or steps of themethods, of the invention. The system may also comprise acomputer-readable memory loaded with executable instructions forperforming the steps of any of the methods of the invention.

In particular, the methods of deriving the radiomic signature may beperformed on such a system and such systems are therefore provided inaccordance with the invention. For example, the system may be configuredto receive, and optionally store, a dataset comprising the values of aplurality of radiomic features of a PVR obtained from medical imagingdata for each of a plurality of individuals, and information regardingthe occurrence during a subsequent period after collection of themedical imaging data of a clinical endpoint indicative of cardiovascularrisk for each of the plurality of individuals. The system may beconfigured to use such a dataset to construct (e.g. derive and validate)a radiomic signature according to the methods of the invention.

Alternatively, the system may be configured to perform the method ofcharacterising a PVR. In particular, the invention provides a system forcharacterising a PVR using medical imaging data of a subject. The systemmay be configured to calculate the value of a radiomic signature of aPVR using the medical imaging data. The radiomic signature may becalculated on the basis of measured values of at least two radiomicfeatures of the PVR, and the measured values of the at least tworadiomic features may be calculated from the medical imaging data.

The system may also be configured to calculate the radiomic featuresfrom medical imaging data, as described in more detail above. The systemmay therefore be configured to receive, and optionally store, medicalimaging data, and to process the imaging data to calculate the radiomicfeatures.

Definition of Radiomic Features

The definitions of the radiomic features referred to herein aregenerally well understood within the field of radiomics by reference totheir name only. However, for ease or reference definitions of thefeatures used herein are provided in Tables R1 to R7 below. The radiomicfeatures in Tables R1 to R7 are defined in accordance with the radiomicfeatures used by the Pyradiomics package(http://pyradiomics.readthedocs.io/en/latest/features.html, see vanGriethuysen, J. J. M., Fedorov, A., Parmar, C., Hosny, A., Aucoin, N.,Narayan, V., Beets-Tan, R. G. H., Fillon-Robin, J. C., Pieper, S.,Aerts, H. J. W. L. (2017). Computational Radiomics System to Decode theRadiographic Phenotype. Cancer Research, 77(21), e104-e107.https://doi.org/10.1158/0008-5472.CAN-17-0339). Most features defined inTables R1 to R7 are in compliance with feature definitions as describedby the Imaging Biomarker Standardization Initiative (IBSI), which areavailable in Zwanenburg et al. (2016) (Zwanenburg, A., Leger, S.,Vallières, M., and Lock, S. (2016). Image biomarker standardisationinitiative—feature definitions. In eprint arXiv:1612.07003 [cs.CV]).Where a definition provided below does not comply exactly from the IBSIdefinition, it should be understood that either definition could be usedin accordance with the invention. Ultimately, the precise mathematicaldefinition of the radiomic features is not crucial because slightmodifications do not affect the general properties of the image that aremeasured by each of the features. Thus, slight modifications to thefeatures (for example, the addition or subtraction of constants orscaling) and alternative definitions of the features are intended to beencompassed by the present invention.

a. First Order Statistics

These statistics describe the central tendency, variability, uniformity,asymmetry, skewness and magnitude of the attenuation values in a givenregion of interest (ROI), disregarding the spatial relationship of theindividual voxels. As such, they describe quantitative and qualitativefeatures of the whole ROI (PVR). A total of 19 features were calculatedfor each one of the eight wavelet transformations and the original CTimage, as follows:

Let:

-   -   X be the attenuation or radiodensity values (e.g. in HU) of a        set of N_(p) voxels included in the region of interest (ROI)    -   P(i) be the first order histogram with N_(g) discrete intensity        levels, where N_(g) is the number of non-zero bins, equally        spaced from 0 with a width.    -   p(i) be the normalized first order histogram and equal to

$\frac{P(i)}{N_{p}}$

-   -   c is a value that shifts the intensities to prevent negative        values in X. This ensures that voxels with the lowest gray        values contribute the least to Energy, instead of voxels with        gray level intensity closest to 0. Since the HU range of adipose        tissue (AT) within the PVR (−190 to −30 HU) does not include        zero, c may be set at c=0. Therefore, higher energy corresponds        to less radiodense AT, and therefore a higher lipophilic        content.    -   ϵ is an arbitrarily small positive number (e.g. ≈2.2×10⁻¹⁶)

TABLE R1 First-order radiomic feature for PVR characterization Radiomicfeature Interpretation$\text{Energy} = {\sum\limits_{i = 1}^{N_{p}}\;\left( {{X(i)} + c} \right)^{2}}$Energy is a measure of the magnitude of voxel values in an image. Alarger value implies a greater sum of the squares of these values.$\text{Total Energy} = {V_{voxel}{\sum\limits_{i = 1}^{N_{p}}\;\left( {{X(i)} + c} \right)^{2}}}$Total Energy is the value of Energy feature scaled by the volume of thevoxel in cubic mm.$\text{Entropy} = {- {\sum\limits_{i = 1}^{N_{g}}\;{{p(i)}{\log_{2}\left( {{p(i)} + \epsilon} \right)}}}}$Entropy specifies the uncertainty/randomness in the image values. Itmeasures the average amount of information required to encode the imagevalues Minimum = min (X) The minimum gray level intensity within theROI. The 10th percentile of X The 10th percentile of X The 90thpercentile of X The 90th percentile of X Maximum = max (X) The maximumgray level intensity within the ROI.${Mean} = {\frac{1}{N_{p}\;}{\sum\limits_{i = 1}^{N_{p}}\;{X(i)}}}$ Theaverage (mean) gray level intensity within the ROI. Median The mediangray level intensity within the ROI. Interquartile range = P₇₅ − P₂₅Here P₂₅ and P₇₅ are the 25^(th) and 75^(th) percentile of the imagearray, respectively. Range = max (X) − min (X) The range of gray valuesin the ROI.${M\; A\; D} = {\frac{1}{N_{p}}{\sum\limits_{i = 1}^{N_{p}}\;{{{X(i)} - \overset{\_}{X}}}}}$Mean Absolute Deviation (MAD) is the mean distance of all intensityvalues from the Mean Value of the image array.$\quad{\quad{\quad\begin{matrix}{{r\; M\; A\; D} =} \\{\frac{1}{N_{10 - 90}}{\sum\limits_{i = 1}^{N_{10 - 90}}\;{{{X_{10 - 90}(i)} - {\overset{\_}{X}}_{10 - 90}}}}}\end{matrix}}}$ Robust Mean Absolute Deviation (rMAD) is the meandistance of all intensity values from the Mean Value calculated on thesubset of image array with gray levels in between, or equal to the10^(th) and 90^(th) percentile.${RMS} = \sqrt{\frac{1}{N_{p}}{\sum\limits_{i = 1}^{N_{p}}\;\left( {{X(i)} + c} \right)^{2}}}$Root Mean Squared (RMS) is the square- root of the mean of all thesquared intensity values. It is another measure of the magnitude of theimage values. This feature is volume-confounded, a larger value of cincreases the effect of volume- confounding. $\quad\begin{matrix}{\text{Skewness} =} \\{\frac{\mu_{3}}{\sigma^{3}} = \frac{\frac{1}{N_{p}}{\sum_{i = 1}^{N_{p}}\left( {{X(i)} - \overset{\_}{X}} \right)^{3}}}{\left( \sqrt{\frac{1}{N_{p}}{\sum_{i = 1}^{N_{p}}\left( {{X(i)} - \overset{\_}{X}} \right)^{2}}} \right)^{3}}}\end{matrix}$ Skewness measures the asymmetry of the distribution ofvalues about the Mean value. Depending on where the tail is elongatedand the mass of the distribution is concentrated, this value can bepositive or negative. (Where μ₃ is the 3^(rd) central moment).$\quad\begin{matrix}{\text{Kurtosis} =} \\{\frac{\mu_{4}}{\sigma^{4}} = \frac{\frac{1}{N_{p}}{\sum_{i = 1}^{N_{p}}\left( {{X(i)} - \overset{\_}{X}} \right)^{4}}}{\left( {\frac{1}{N_{p}}{\sum_{i = 1}^{N_{p}}\left( {{X(i)} - \overset{\_}{X}} \right)^{2}}} \right)^{2}}}\end{matrix}$ Kurtosis is a measure of the ‘peakedness’ of thedistribution of values in the image ROI. A higher kurtosis implies thatthe mass of the distribution is concentrated towards the tail(s) ratherthan towards the mean. A lower kurtosis implies the reverse: that themass of the distribution is concentrated towards a spike near the Meanvalue. (Where μ₄ is the 4th central moment).$\text{Variance} = {\frac{1}{N_{p}}{\sum\limits_{i = 1}^{N_{p}}\;\left( {{X(i)} - \overset{\_}{X}} \right)^{2}}}$Variance is the mean of the squared distances of each intensity valuefrom the Mean value. This is a measure of the spread of the distributionabout the mean.$\text{Uniformity} = {\sum\limits_{i = 1}^{N_{g}}\;{p(i)}^{2}}$Uniformity is a measure of the sum of the squares of each intensityvalue. This is a measure of the heterogeneity of the image array, wherea greater uniformity implies a greater heterogeneity or a greater rangeof discrete intensity values.

b. Shape-Related Statistics

Shape-related statistics describe the size and shape of a given ROI,without taking into account the attenuation values of its voxels. Sincethey are independent of the gray level intensities, shape-relatedstatistics were consistent across all wavelet transformation and theoriginal CT image, and therefore were only calculated once. These weredefined as follows:

Let:

V be the volume of the ROI in mm³A be the surface area of the ROI in mm²

TABLE R2 Shape-related radiomic features for PVR characterizationRadiomic feature Interpretation$\text{Volume} = {\sum\limits_{i = 1}^{N}\; V_{i}}$ The volume of theROI V is approximated by multiplying the number of voxels in the ROI bythe volume of a single voxel V_(i).$\text{Surface Area} = {\sum\limits_{i = 1}^{N}\;{\frac{1}{2}{{a_{i}b_{i} \times a_{i}c_{i}}}}}$Surface Area is an approximation of the surface of the ROI in mm²,calculated using a marching cubes algorithm, where N is the number oftriangles forming the surface mesh of the volume (ROI), a_(i)b_(i) anda_(i)c_(i) arc the edges of the i^(th) triangle formed by points a_(i),b_(i) and c_(i). $\text{Surface to volume ratio} = \frac{A}{V}$ Here, alower value indicates a more compact (sphere-like) shape. This featureis not dimensionless, and is therefore (partly) dependent on the volumeof the ROI. $\text{Sphericity} = \frac{\sqrt[3]{36\pi\; V^{2}}}{A}$Sphericity is a measure of the roundness of the shape of the tumorregion relative to a sphere. It is a dimensionless measure, independentof scale and orientation. The value range is 0 < sphericity ≤ 1, where avalue of 1 indicates a perfect sphere (a sphere has the smallestpossible surface area for a given volume, compared to other solids).Volume Number Total number of discrete volumes in the ROI. Voxel NumberTotal number of discrete voxels in the ROI. Maximum 3D diameter Maximum3D diameter is defined as the largest pairwise Euclidean distancebetween surface voxels in the ROI (Feret Diameter). Maximum 2D diameter(Slice) Maximum 2D diameter (Slice) is defined as the largest pairwiseEuclidean distance between ROI surface voxels in the row-column(generally the axial) plane. Maximum 2D diameter (Column) Maximum 2Ddiameter (Column) is defined as the largest pairwise Euclidean distancebetween ROI surface voxels in the row-slice (usually the coronal) plane.Maximum 2D diameter (Row) Maximum 2D diameter (Row) is defined as thelargest pairwise Euclidean distance between tumor surface voxels in thecolumn-slice (usually the sagittal) plane.$\text{Major axis} = {4\sqrt{\lambda_{major}}}$ λ_(major) is the lengthof the largest principal component axis$\text{Minor axis} = {4\sqrt{\lambda_{minor}}}$ λ_(minor) is the lengthof the second largest principal component axis$\text{Least axis} = {4\sqrt{\lambda_{least}}}$ λ_(least) is the lengthof the smallest principal component axis$\text{Elongation} = \sqrt{\frac{\lambda_{minor}}{\lambda_{major}}}$Here, λ_(major) and λ_(minor) ate the lengths of the largest and secondlargest principal component axes. The values range between 1(circle-like (non-elongated)) and 0 (single point or 1 dimensionalline). ${Flatness} = \sqrt{\frac{\lambda_{least}}{\lambda_{major}}}$Here, λ_(major) and λ_(minor) are the lengths of the largest andsmallest principal component axes. The values range between 1 (non-flat,sphcrc- like) and 0 (a flat object).

c. Gray Level Co-Occurrence Matrix (GLCM)

In simple words, a GLCM describes the number of times a voxel of a givenattenuation value i is located next to a voxel of j. A GLCM of sizeN_(g)×N_(g) describes the second-order joint probability function of animage region constrained by the mask and is defined as P(i,j|δ,θ). The(i,j)^(th) element of this matrix represents the number of times thecombination of levels i and j occur in two pixels in the image, that areseparated by a distance of δ pixels along angle θ. The distance δ fromthe center voxel is defined as the distance according to the infinitynorm. For δ=1, this results in 2 neighbors for each of 13 angles in 3D(26-connectivity) and for δ=2 a 98-connectivity (49 unique angles). Inorder to get rotationally invariant results, statistics are calculatedin all directions and then averaged, to ensure a symmetrical GLCM.

Let:

ϵ be an arbitrarily small positive number (e.g. ≈22.2×10⁻¹⁶)P(i,j) be the co-occurrence matrix for an arbitrary δ and θp(i,j) be the normalized co-occurrence matrix and equal to

$\frac{P\left( {i,j} \right)}{\Sigma\;{P\left( {i,j} \right)}}$

Ng be the number of discrete intensity levels in the imagep_(x)(i)=Σ_(j=1) ^(N) ^(g) P(i,j) be the marginal row probabilitiesp_(y)(j)=Σ_(i=1) ^(N) ^(g) P(i,j) be the marginal column probabilitiesμ_(x) be the mean gray level intensity of p_(x) and defined asμ_(x)=Σ_(i=1) ^(N) ^(g) p_(x)(i)iμ_(y) be the mean gray level intensity of p_(y) and defined asμ_(y)=Σ_(j=1) ^(N) ^(g) p_(y)(j)jσ_(x) be the standard deviation of p_(x)σ_(y) be the standard deviation of p_(y)

${{p_{x + y}(k)} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{p\left( {i,j} \right)}}}},$

where i+j=k, and k=2, 3, . . . , 2N_(g)

${{p_{x - y}(k)} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{p\left( {i,j} \right)}}}},$

where |i−j|=k, and k=0, 1, . . . , N_(g)−1HX=−Σ_(i=1) ^(N) ^(g) p_(x)(i)log₂(p_(x)(i)+ϵ) be the entropy of p_(x)HY=−Σ_(j=1) ^(N) ^(g) p_(y)(j)log₂(p_(y)(j)+ϵ) be the entropy of p_(y)

${{HXY}\; 1} = {- {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{{p\left( {i,j} \right)}{\log_{2}\left( {{p_{x}(i)},{{p_{y}(j)} + \epsilon}} \right)}}}}}$${{HXY}\; 2} = {- {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}{{p_{x}(i)}{p_{y}(j)}{\log_{2}\left( {{{p_{x}(i)}{p_{y}(j)}} + \epsilon} \right)}}}}}$

For distance weighting, GLCM matrices are weighted by weighting factor Wand then summed and normalised. Weighting factor W is calculated for thedistance between neighbouring voxels by W=e^(−∥d∥) ² , where d is thedistance for the associated angle.

TABLE R3 Gray Level Co-occurrence Matrix (GLCM) statistics for PVRcharacterization Radiomic feature Interpretation${Autocorrelation} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{{p\left( {i,j} \right)}{ij}}}}$Autocorrelation is a measure of the magnitude of the fineness andcoarseness of texture.$\text{Joint average} = {\mu_{x} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{{p\left( {i,j} \right)}i}}}}$Returns the mean gray level intensity of the i distribution.$\quad\begin{matrix}{\text{Cluster prominence} =} \\{\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{\left( {i + j - \mu_{x} - \mu_{y}} \right)^{4}{p\left( {i,j} \right)}}}}\end{matrix}$ Cluster Prominence is a measure of the skewness andasymmetry of the GLCM. A higher value implies more asymmetry around themean while a lower value indicates a peak near the mean value and lessvariation around the mean. $\quad\begin{matrix}{\text{Cluster tendency} =} \\{\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{\left( {i + j - \mu_{x} - \mu_{y}} \right)^{2}{p\left( {i,j} \right)}}}}\end{matrix}$ Cluster Tendency is a measure of groupings of voxels withsimilar gray-level values. $\quad\begin{matrix}{\text{Cluster shade} =} \\{\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{\left( {i + j - \mu_{x} - \mu_{y}} \right)^{3}{p\left( {i,j} \right)}}}}\end{matrix}$ Cluster Shade is a measure of the skewness and uniformityof the GLCM. A higher cluster shade implies greater asymmetry about themean.$\text{Contrast} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{\left( {i - j} \right)^{2}{p\left( {i,j} \right)}}}}$Contrast is a measure of the local intensity variation, favoring valuesaway from the diagonal (i = j). A larger value correlates with a greaterdisparity in intensity values among neighboring voxels.$\quad\begin{matrix}{\text{Correlation} =} \\\frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {{\sum_{j = 1}^{N_{g}}{{p\left( {i,j} \right)}{ij}}} - {\mu_{x}\mu_{y}}}\end{matrix}}{{\sigma_{x}(i)}{\sigma_{y}(j)}}\end{matrix}$ Correlation is a value between 0 (uncorrelated) and 1(perfectly correlated) showing the linear dependency of gray levelvalues to their respective voxels in the GLCM.$\text{Difference average} = {\sum\limits_{k = 0}^{N_{g} - 1}\;{{kp}_{x - y}(k)}}$Difference Average measures the relationship between occurrences ofpairs with similar intensity values and occurrences of pairs withdiffering intensity values. $\quad\begin{matrix}{\text{Difference entropy} =} \\{\sum\limits_{k = 0}^{N_{g} - 1}{{p_{x - y}(k)}{\log_{2}\left( {{p_{x - y}(k)} + \epsilon} \right)}}}\end{matrix}$ Difference Entropy is a measure of therandomness/variability in neighborhood intensity value differences.$\quad\begin{matrix}{\text{Difference variance} =} \\{\sum\limits_{k = 0}^{N_{g} - 1}{\left( {k - {DA}} \right)^{2}{p_{x - y}(k)}}}\end{matrix}$ Difference Variance is a measure of heterogeneity thatplaces higher weights on differing intensity level pairs that deviatemore from the mean.$\text{Joint energy} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;\left( {p\left( {i,j} \right)} \right)^{2}}}$Joint energy is a measure of homogeneous patterns in the image. Agreater joint energy implies that there are more instances of intensityvalue pairs in the image that neighbor each other at higher frequencies.(also known as Angular Second Moment). $\quad\begin{matrix}{\text{Joint entropy} =} \\{- {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{{p\left( {i,j} \right)}{\log_{2}\left( {{p\left( {i,j} \right)} + \epsilon} \right)}}}}}\end{matrix}$ Joint entropy is a measure of the randomness/variabilityin neighborhood intensity values.${I\; M\; C\mspace{14mu} 1} = \frac{{HXY} - {{HXY}\; 1}}{\max\left\{ {{HX},{HY}} \right\}}$Informational measure of correlation 1 IMC 2 = {square root over (1 −e^(−2(HXY2-HXY)))} Informational measure of correlation 2${I\; D\; M} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;\frac{p\left( {i,j} \right)}{\left. {1 +} \middle| {i - j} \right|^{2}}}}$IDM (inverse difference moment a.k.a Homogeneity 2) is a measure of thelocal homogeneity of an image. IDM weights are the inverse of theContrast weights (decreasing exponentially from the diagonal i = j inthe GLCM).${I\; D\; M\; N} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;\frac{p\left( {i,j} \right)}{1 + \left( \frac{\left| {i - j} \right|^{2}}{N_{g}^{2}} \right)}}}$IDMN (inverse difference moment normalized) is a measure of the localhomogeneity of an image. IDMN weights are the inverse of the Contrastweights (decreasing exponentially from the diagonal i = j in the GLCM).Unlike Homogeneity 2, IDMN normalizes the square of the differencebetween neighboring intensity values by dividing over the square of thetotal number of discrete intensity values.${I\; D} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;\frac{p\left( {i,j} \right)}{\left. {1 +} \middle| {i - j} \right|}}}$ID (inverse difference a.k.a. Homogeneity 1) is another measure of thelocal homogeneity of an image. With more uniform gray levels, thedenominator will remain low, resulting in a higher overall value.${I\; D\; N} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;\frac{p\left( {i,j} \right)}{1 + \left( \frac{{i - j}}{N_{g}} \right)}}}$IDN (inverse difference normalized) is another measure of the localhomogeneity of an image. Unlike Homogeneity 1, IDN normalizes thedifference between the neighboring intensity values by dividing over thetotal number of discrete intensity values. $\quad\begin{matrix}{\text{Inverse variance} =} \\{{\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;\frac{p\left( {i,j} \right)}{{{i - j}}^{2}}}},{i \neq j}}\end{matrix}$ Maximum probability = max (p(i, j)) Maximum Probability isoccurrences of the most predominant pair of neighboring intensity values(also known as Joint maximum).$\text{Sum average} = {\sum\limits_{k = 2}^{2N_{g}}\;{{p_{x + y}(k)}k}}$Sum Average measures the relationship between occurrences of pairs withlower intensity values and occurrences of pairs with higher intensityvalues. $\quad\begin{matrix}{\text{Sum entropy} =} \\{\sum\limits_{k = 2}^{2N_{g}}\;{{p_{x + y}(k)}{\log_{2}\left( {{p_{x + y}(k)} + \epsilon} \right)}}}\end{matrix}$ Sum Entropy is a sum of neighborhood intensity valuedifferences.$\text{Sum squares} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{\left( {i - \mu_{x}} \right)^{2}{p\left( {i,j} \right)}}}}$Sum of Squares or Variance is a measure in the distribution ofneighboring intensity level pairs about the mean intensity level in theGLCM. (Defined by IBSI as Joint Variance).

d. Gray Level Size Zone Matrix (GLSZM)

A Gray Level Size Zone (GLSZM) describes gray level zones in a ROI,which are defined as the number of connected voxels that share the samegray level intensity. A voxel is considered connected if the distance is1 according to the infinity norm (26-connected region in a 3D,8-connected region in 2D). In a gray level size zone matrix P(i,j) the(i,j)^(th) element equals the number of zones with gray level i and sizej appear in image. Contrary to GLCM and GLRLM, the GLSZM is rotationindependent, with only one matrix calculated for all directions in theROI.

Let:

N_(g) be the number of discreet intensity values in the imageN_(s) be the number of discreet zone sizes in the imageN_(p) be the number of voxels in the imageN, be the number of zones in the ROI, which is equal to Σ_(i=1) ^(N)^(g) Σ_(j=1) ^(N) ^(s) P(i,j) and 1≤N_(z)≤N_(p)P(i,j) be the size zone matrixp(i,j) be the normalized size zone matrix, defined as

${p\left( {i,j} \right)} = \frac{P\left( {i,j} \right)}{N_{z}}$

ϵ is an arbitrarily small positive number (e.g. ≈2.2×10⁻¹⁶).

TABLE R4 Gray Level Size Zone Matrix (GLSZM) statistics for PVRcharacterization Radiomic feature Interpretation${S\; A\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{s}}\frac{P\left( {i,j} \right)}{j^{2}}}\end{matrix}}{N_{z}}$ SAE (small area emphasis) is a measure of thedistribution of small size zones, with a greater value indicative ofsmaller size zones and more fine textures.${L\; A\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{s}}{{P\left( {i,j} \right)}j^{2}}}\end{matrix}}{N_{z}}$ LAE (large area emphasis) is a measure of thedistribution of large area size zones, with a greater value indicativeof larger size zones and more coarse textures.${G\; L\; N} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & \left( {\sum_{j = 1}^{N_{s}}{P\left( {i,j} \right)}} \right)^{2}\end{matrix}}{N_{z}}$ GLN (gray level non-uniformity) measures thevariability of gray-level intensity values in the image, with a lowervalue indicating more homogeneity in intensity values.${G\; L\; N\; N} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & \left( {\sum_{j = 1}^{N_{s}}{P\left( {i,j} \right)}} \right)^{2}\end{matrix}}{N_{z}^{2}}$ GLNN (gray level non-uniformity normalized)measures the variability of gray-level intensity values in the image,with a lower value indicating a greater similarity in intensity values.This is the normalized version of the GLN formula.${S\; Z\; N} = \frac{\begin{matrix}\sum_{j = 1}^{N_{s}} & \left( {\sum_{i = 1}^{N_{g}}{P\left( {i,j} \right)}} \right)^{2}\end{matrix}}{N_{z}}$ SZN (size zone non-uniformity) measures thevariability of size zone volumes in the image, with a lower valueindicating more homogeneity in size zone volumes.${S\; Z\; N\; N} = \frac{\begin{matrix}\sum_{j = 1}^{N_{s}} & \left( {\sum_{i = 1}^{N_{g}}{P\left( {i,j} \right)}} \right)^{2}\end{matrix}}{N_{z}^{2}}$ SZNN (size zone non-uniformity normalized)measures the variability of size zone volumes throughout the image, witha lower value indicating more homogeneity among zone size volumes in theimage. This is the normalized version of the SZN formula.$\text{Zone Percentage} = \frac{N_{z}}{N_{p}}$ ZP (Zone Percentage)measures the coarseness of the texture by taking the ratio of number ofzones and number of voxels in the ROI. Values are in range${\frac{1}{N_{p}} \leq {ZP} \leq 1},\text{with~~higher~~values}$indicating a larger portion of the ROI consists of small zones(indicates a more fine texture). GLV = Σ_(i=1) ^(N) ^(g) Σ_(j=1) ^(N)^(s) p(i, j)(i − μ)², Gray level variance (GLV) measures where μ =Σ_(i=1) ^(N) ^(g) Σ_(j=1) ^(N) ^(s) p(i, j)i the variance in gray levelintensities for the zones. ZV = Σ_(i=1) ^(N) ^(g) Σ_(j=1) ^(N) ^(s) p(i,j)(j − μ)², Zone Variance (ZV) measures the where μ = Σ_(i=1) ^(N) ^(g)Σ_(j=1) ^(N) ^(s) p(i, j)j variance in zone size volumes for the zones.${Z\; E} = {- {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{s}}\;{{p\left( {i,j} \right)}{\log_{2}\left( {{p\left( {i,j} \right)} + \epsilon} \right)}}}}}$Zone Entropy (ZE) measures the uncertainty/randomness in thedistribution of zone sizes and gray levels. A higher value indicatesmore heterogeneneity in the texture patterns.${L\; G\; L\; Z\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{s}}\frac{P\left( {i,j} \right)}{i^{2}}}\end{matrix}}{N_{z}}$ LGLZE (low gray level zone emphasis) measures thedistribution of lower gray- level size zones, with a higher valueindicating a greater proportion of lower gray-level values and sizezones in the image. ${H\; G\; L\; Z\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{s}}{{P\left( {i,j} \right)}i^{2}}}\end{matrix}}{N_{z}}$ HGLZE (high gray level zone emphasis) measures thedistribution of the higher gray-level values, with a higher valueindicating a greater proportion of higher gray-level values and sizezones in the image. ${S\; A\; L\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{s}}\frac{P\left( {i,j} \right)}{i^{2}j^{2}}}\end{matrix}}{N_{z}}$ SALGLE (small area low gray level emphasis)measures the proportion in the image of the joint distribution ofsmaller size zones with lower gray-level values.${S\; A\; H\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{s}}\frac{{P\left( {i,j} \right)}i^{2}}{j^{2}}}\end{matrix}}{N_{z}}$ SAHGLE (small area high gray level emphasis)measures the proportion in the image of the joint distribution ofsmaller size zones with higher gray-level values.${L\; A\; L\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{s}}\frac{{P\left( {i,j} \right)}j^{2}}{i^{2}}}\end{matrix}}{N_{z}}$ LALGLE (low area low gray level emphasis) measuresthe proportion in the image of the joint distribution of larger sizezones with lower gray-level values.${L\; A\; H\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{s}}{{P\left( {i,j} \right)}i^{2}j^{2}}}\end{matrix}}{N_{z}}$ LAHGLE (low area high gray level emphasis)measures the proportion in the image of the joint distribution of largersize zones with higher gray-level values.

e. Gray Level Run Length Matrix (GLRLM)

A Gray Level Run Length Matrix (GLRLM) describes gray level runs, whichare defined as the length in number of pixels, of consecutive pixelsthat have the same gray level value. In a gray level run length matrixP(i,j|θ), the (i,j)^(th) element describes the number of runs with graylevel i and length j occur in the image (ROI) along angle θ.

Let:

N_(g) be the number of discreet intensity values in the imageN_(r) be the number of discreet run lengths in the imageN_(p) be the number of voxels in the imageN_(z)(θ) be the number of runs in the image along angle θ, which isequal to Σ_(i=1) ^(N) ^(g) Σ_(j=1) ^(N) ^(r) P(i,j|θ) and1≤N_(z)(θ)≤N_(p)P(i,j|θ) be the run length matrix for an arbitrary direction θp(i,j|θ) be the normalized run length matrix, defined as

${p\left( {i,{j❘\theta}} \right)} = \frac{P\left( {i,{j❘\theta}} \right)}{N_{z}(\theta)}$

ϵ is an arbitrarily small positive number (e.g. ≈2.2×10⁻¹⁶).

By default, the value of a feature is calculated on the GLRLM for eachangle separately, after which the mean of these values is returned. Ifdistance weighting is enabled, GLRLMs are weighted by the distancebetween neighbouring voxels and then summed and normalised. Features arethen calculated on the resultant matrix. The distance betweenneighbouring voxels is calculated for each angle using the normspecified in ‘weightingNorm’

TABLE R5 Gray Level Run Length Matrix (GLRLM) statistics for PVRcharacterization Radiomic feature Interpretation${S\; R\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{r}}\frac{P\left( {i,{j\text{|}\theta}} \right)}{j^{2}}}\end{matrix}}{N_{z}(\theta)}$ SRE (Short Run Emphasis) is a measure ofthe distribution of short run lengths, with a greater value indicativeof shorter run lengths and more fine textural textures.${L\; R\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{r}}{{P\left( {i,{j\text{|}\theta}} \right)}j^{2}}}\end{matrix}}{N_{z}(\theta)}$ LRE (Long Run Emphasis) is a measure ofthe distribution of long run lengths, with a greater value indicative oflonger run lengths and more coarse structural textures.${G\; L\; N} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & \left( {\sum_{j = 1}^{N_{r}}{P\left( {i,{j\text{|}\theta}} \right)}} \right)^{2}\end{matrix}}{N_{z}(\theta)}$ GLN(Gray Level Non- uniformity) measuresthe similarity of gray-level intensity values in the image, where alower GLN value correlates with a greater similarity in intensityvalues. ${G\; L\; N\; N} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & \left( {\sum_{j = 1}^{N_{r}}{P\left( {i,{j\text{|}\theta}} \right)}} \right)^{2}\end{matrix}}{{N_{z}(\theta)}^{2}}$ GLNN (Gray Level Non- uniformityNormalized) measures the similarity of gray-level intensity values inthe image, where a lower GLNN value correlates with a greater similarityin intensity values. This is the normalized version of the GLN formula.${R\; L\; N} = \frac{\begin{matrix}\sum_{j = 1}^{N_{r}} & \left( {\sum_{i = 1}^{N_{g}}{P\left( {i,{j\text{|}\theta}} \right)}} \right)^{2}\end{matrix}}{N_{z}(\theta)}$ RLN (Run Length Non- uniformity) measuresthe similarity of run lengths throughout the image, with a lower valueindicating more homogeneity among run lengths in the image.${R\; L\; N\; N} = \frac{\begin{matrix}\sum_{j = 1}^{N_{r}} & \left( {\sum_{i = 1}^{N_{g}}{P\left( {i,{j\text{|}\theta}} \right)}} \right)^{2}\end{matrix}}{N_{z}}$ RLNN (Run Length Non- uniformity) measures thesimilarity of run lengths throughout the image, with a lower valueindicating more homogeneity among run lengths in the image. This is thenormalized version of the RLN formula.${R\; P} = \frac{N_{z}(\theta)}{N_{p}}$ RP (Run Percentage) measures thecoarseness of the texture by taking the ratio of number of runs andnumber of voxels in the ROI. Values are in range${\frac{1}{N_{p}} \leq {RP} \leq 1},\text{with higher}$ valuesindicating a larger portion of the ROI consists of short runs (indicatesa more fine texture). GLV = Σ_(i=1) ^(N) ^(g) Σ_(j=1) ^(N) ^(r) p(i,j|θ)(i − μ)², GLV (Gray Level where μ = Σ_(i=1) ^(N) ^(g) Σ_(j=1) ^(N)^(r) p(i, j|θ)i Variance) measures the variance in gray level intensityfor the runs. RV = Σ_(i=1) ^(N) ^(g) Σ_(j=1) ^(N) ^(r) p(i, j|θ)(j −μ)², RV (Run Variance) is a where μ = Σ_(i=1) ^(N) ^(g) Σ_(j=1) ^(N)^(r) p(i, j|θ)j measure of the variance in runs for the run lengths.${R\; E} = {- {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{r}}\;{{p\left( {i,{j\text{|}\theta}} \right)}{\log_{2}\left( {{p\left( {i,{j\text{|}\theta}} \right)} + \epsilon} \right)}}}}}$RE (Run Entropy) measures the uncertainty/randomness in the distributionof run lengths and gray levels. A higher value indicates moreheterogeneity in the texture patterns.${L\; G\; L\; R\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{r}}\frac{P\left( {i,{j\text{|}\theta}} \right)}{i^{2}}}\end{matrix}}{N_{z}(\theta)}$ LGLRE (low gray level run emphasis)measures the distribution of low gray-level values, with a higher valueindicating a greater concentration of low gray-level values in theimage. ${H\; G\; L\; R\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{r}}{{P\left( {i,{j\text{|}\theta}} \right)}i^{2}}}\end{matrix}}{N_{z}(\theta)}$ HGLRE (high gray level run emphasis)measures the distribution of the higher gray-level values, with a highervalue indicating a greater concentration of high gray- level values inthe image. ${S\; R\; L\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{r}}\frac{P\left( {i,{j\text{|}\theta}} \right)}{i^{2}j^{2}}}\end{matrix}}{N_{z}(\theta)}$ SRLGLE (short run low gray level emphasis)measures the joint distribution of shorter run lengths with lower gray-level values. ${S\; R\; H\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{r}}\frac{{P\left( {i,{j\text{|}\theta}} \right)}i^{2}}{j^{2}}}\end{matrix}}{N_{z}(\theta)}$ SRHGLE (short run high gray levelemphasis) measures the joint distribution of shorter run lengths withhigher gray- level values.${L\; R\; L\; G\; L\; R\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{r}}\frac{{P\left( {i,{j\text{|}\theta}} \right)}j^{2}}{i^{2}}}\end{matrix}}{N_{z}(\theta)}$ LRLGLRE (long run low gray level emphasis)measures the joint distribution of long run lengths with lower gray-level values. ${L\; R\; H\; G\; L\; R\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{r}}{{P\left( {i,{j\text{|}\theta}} \right)}i^{2}j^{2}}}\end{matrix}}{N_{z}(\theta)}$ LRHGLRE (long run high gray level runemphasis) measures the joint distribution of long run lengths withhigher gray- level values.

f. Neighbouring Gray Tone Difference Matrix (NGTDM) Features

A Neighbouring Gray Tone Difference Matrix quantifies the differencebetween a gray value and the average gray value of its neighbours withindistance δ. The sum of absolute differences for gray level i is storedin the matrix. Let X_(gl) be a set of segmented voxels andx_(gl)(j_(x),j_(y),j_(z))∈X_(gl) be the gray level of a voxel atposition (j_(x),j_(y),j_(z)), then the average gray level of theneigbourhood is:

${{\overset{\_}{A}}_{i} = {{\overset{\_}{A}\left( {j_{x},j_{y},j_{z}} \right)} = {\frac{1}{W}{\sum\limits_{k_{x} = {- \delta}}^{\delta}\;{\sum\limits_{k_{y} = {- \delta}}^{\delta}\;{\sum\limits_{k_{z} = {- \delta}}^{\delta}\;{x_{gl}\left( {{j_{x} + k_{x}},{j_{y} + k_{y}},{j_{z} + k_{z}}} \right)}}}}}}},{{{{where}\mspace{14mu}\left( {k_{x},k_{y},k_{z}} \right)} \neq {\left( {0,0,0} \right)\mspace{14mu}{and}\mspace{14mu}{x_{gl}\left( {{j_{x} + k_{x}},{j_{y} + k_{y}},{j_{z} + k_{z}}} \right)}}} \in x_{gl}}$

Here, W is the number of voxels in the neighbourhood that are also inX_(gl).

Let:

n_(i) be the number of voxels in X_(gl) with gray level iNv,p be the total number of voxels in X_(gl) and equal to Σn_(i) (i.e.the number of voxels with a valid region; at least 1 neighbor).N_(v,p)≤N_(p), where N_(p) is the total number of voxels in the ROI.p_(i) be the gray level probability and equal to n_(i)/N_(v)

$s_{i} = \left\{ {\begin{matrix}{\Sigma^{n_{i}}{{i - {\overset{\_}{A}}_{i}}}} & {for} & {n_{i} \neq 0} \\{0} & {for} & {n_{i} = 0}\end{matrix}\mspace{14mu}{be}\mspace{14mu}{the}\mspace{14mu}{sum}\mspace{14mu}{of}\mspace{14mu}{absolute}\mspace{14mu}{differences}\mspace{14mu}{for}\mspace{14mu}{gray}\mspace{14mu}{level}\mspace{14mu} i} \right.$

N_(g) be the number of discreet gray levelsN_(g,p) be the number of gray levels where p_(i)≠0

TABLE R6 Neigbouring Gray Tone Difference Matrix (NGTDM) for PVRcharacterization Radiomic feature Interpretation${Coarseness} = \frac{1}{\sum_{i = 1}^{N_{g}}{p_{i}s_{i}}}$ Coarsenessis a measure of average difference between the center voxel and itsneighbourhood and is an indication of the spatial rate of change. Ahigher value indicates a lower spatial change rate and a locally moreuniform texture. $\quad\begin{matrix}{{\text{Contrast} = {\left( {\frac{1}{N_{g,p}\left( {N_{g,p} - 1} \right)}{\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{p_{i}{p_{j}\left( {i - j} \right)}^{2}}}}} \right)\left( {\frac{1}{N_{v,p}}{\sum\limits_{i = 1}^{N_{g}}\; s_{i}}} \right)}},} \\{{{{where}\mspace{14mu} p_{i}} \neq 0},{p_{j} \neq 0}}\end{matrix}$ Contrast is a measure of the spatial intensity change, butis also dependent on the overall gray level dynamic range. Contrast ishigh when both the dynamic range and the spatial change rate are high,i.e. an image with a large range of gray levels, with large changesbetween voxels and their neighbourhood. $\quad\begin{matrix}{{\text{Busyness} = \frac{\sum_{i = 1}^{N_{g}}{p_{i}s_{i}}}{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{g}}{{{ip}_{i} - {jp}_{j}}}}\end{matrix}}},} \\{{{{where}\mspace{14mu} p_{i}} \neq 0},{p_{j} \neq 0}}\end{matrix}$ A measure of the change from a pixel to its neighbour. Ahigh value for busyness indicates a ‘busy’ image, with rapid changes ofintensity between pixels and its neighbourhood. $\quad{\begin{matrix}{\text{Complexity} = {\frac{1}{N_{v,p}}{\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{g}}\;{{{i - j}}\frac{{p_{i}s_{i}} + {p_{j}s_{j}}}{p_{i} + p_{j}}}}}}} \\{{{{where}\mspace{14mu} p_{i}} \neq 0},{p_{j} \neq 0}}\end{matrix},}$ An image is considered complex when there are manyprimitive components in the image, i.e. the image is non-uniform andthere are many rapid changes in gray level intensity.$\quad{\begin{matrix}{\text{Strength} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{g}}{\left( {p_{i} + p_{j}} \right)\left( {i - j} \right)^{2}}}\end{matrix}}{\sum_{i = 1}^{N_{g}}s_{i}}} \\{{{{where}\mspace{14mu} p_{i}} \neq 0},{p_{j} \neq 0}}\end{matrix},}$ Strength is a measure of the primitives in an image. Itsvalue is high when the primitives are easily defined and visible, i.e.an image with slow change in intensity but more large coarse differencesin gray level intensities.

g. Gray Level Dependence Matrix (GLDM)

A Gray Level Dependence Matrix (GLDM) quantifies gray level dependenciesin an image. A gray level dependency is defined as the number ofconnected voxels within distance δ that are dependent on the centervoxel. A neighbouring voxel with gray level j is considered dependent oncenter voxel with gray level i if |i−j|≤α. In a gray level dependencematrix P(i,j) the (i,j)^(th) element describes the number of times avoxel with gray level i with j dependent voxels in its neighbourhoodappears in image.

N_(g) be the number of discreet intensity values in the imageN_(d) be the number of discreet dependency sizes in the imageN_(z) be the number of dependency zones in the image, which is equal toΣ_(i=1) ^(N) ^(g) Σ_(j=1) ^(N) ^(d) P(i,j)P(i,j) be the dependence matrixp(i,j) be the normalized dependence matrix, defined as

${p\left( {i,j} \right)} = \frac{P\left( {i,j} \right)}{N_{z}}$

TABLE R7 Gray Level Dependence Matrix (GLDM) statistics for PVRcharacterization Radiomic feature Interpretation${S\; D\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{d}}\frac{P\left( {i,j} \right)}{i^{2}}}\end{matrix}}{N_{z}}$ SDE (Small Dependence Emphasis): A measure of thedistribution of small dependencies, with a greater value indicative ofsmaller dependence and less homogeneous textures.${L\; D\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{d}}{{P\left( {i,j} \right)}j^{2}}}\end{matrix}}{N_{z}}$ LDE (Large Dependence Emphasis): A measure of thedistribution of large dependencies, with a greater value indicative oflarger dependence and more homogeneous textures.${G\; L\; N} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & \left( {\sum_{j = 1}^{N_{d}}{P\left( {i,j} \right)}} \right)^{2}\end{matrix}}{\begin{matrix}\sum_{i = 1}^{N_{g}} & \begin{matrix}\sum_{j = 1}^{N_{d}} & {P\left( {i,j} \right)}\end{matrix}\end{matrix}}$ GLN (Gray Level Non-Uniformity): Measures the similarityof gray-level intensity values in the image, where a lower GLN valuecorrelates with a greater similarity in intensity values.${D\; N} = \frac{\begin{matrix}\sum_{j = 1}^{N_{d}} & \left( {\sum_{i = 1}^{N_{g}}{P\left( {i,j} \right)}} \right)^{2}\end{matrix}}{N_{z}}$ DN (Dependence Non-Uniformity): Measures thesimilarity of dependence throughout the image, with a lower valueindicating more homogeneity among dependencies in the image.${D\; N\; N} = \frac{\begin{matrix}\sum_{j = 1}^{N_{d}} & \left( {\sum_{i = 1}^{N_{g}}{P\left( {i,j} \right)}} \right)^{2}\end{matrix}}{N_{z}^{2}}$ DNN (Dependence Non-Uniformity Normalized):Measures the similarity of dependence throughout the image, with a lowervalue indicating more homogeneity among dependencies in the image. Thisis the normalized version of the DLN formula. $\begin{matrix}{{{G\; L\; V} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{d}}\;{{p\left( {i,j} \right)}\left( {i - \mu} \right)^{2}}}}},} \\{{{where}\mspace{14mu}\mu} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{d}}\;{{ip}\left( {i,j} \right)}}}}\end{matrix}$ GLV (Gray Level Variance): Measures the variance in greylevel in the image. $\begin{matrix}{{{D\; V} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{d}}\;{{p\left( {i,j} \right)}\left( {j - \mu} \right)^{2}}}}},} \\{{{where}\mspace{14mu}\mu} = {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{d}}\;{{jp}\left( {i,j} \right)}}}}\end{matrix}$ DV (Dependence Variance): Measures the variance independence size in the image.${D\; E} = {- {\sum\limits_{i = 1}^{N_{g}}\;{\sum\limits_{j = 1}^{N_{d}}\;{{p\left( {i,j} \right)}{\log_{2}\left( {{p\left( {i,j} \right)} + \epsilon} \right)}}}}}$DE (Dependence Entropy): Measures the entropy in dependence size in theimage. ${L\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{d}}\frac{P\left( {i,j} \right)}{i^{2}}}\end{matrix}}{N_{z}}$ LGLE (Low Gray Level Emphasis): Measures thedistribution of low gray- level values, with a higher value indicating agreater concentration of low gray-level values in the image.${H\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{d}}{{P\left( {i,j} \right)}i^{2}}}\end{matrix}}{N_{z}}$ HGLE (High Gray Level Emphasis): Measures thedistribution of the higher gray-level values, with a higher valueindicating a greater concentration of high gray-level values in theimage. ${S\; D\; L\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{d}}\frac{P\left( {i,j} \right)}{i^{2}j^{2}}}\end{matrix}}{N_{z}}$ SDLGLE (Small Dependence Low Gray Level Emphasis):Measures the joint distribution of small dependence with lowergray-level values. ${S\; D\; H\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{d}}\frac{{P\left( {i,j} \right)}i^{2}}{j^{2}}}\end{matrix}}{N_{z}}$ SDHGLE (Small Dependence High Gray LevelEmphasis): Measures the joint distribution of small dependence withhigher gray-level values.${L\; D\; L\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{d}}\frac{{P\left( {i,j} \right)}j^{2}}{i^{2}}}\end{matrix}}{N_{z}}$ LDLGLE (Large Dependence Low Gray Level Emphasis):Measures the joint distribution of large dependence with lowergray-level values. ${L\; D\; H\; G\; L\; E} = \frac{\begin{matrix}\sum_{i = 1}^{N_{g}} & {\sum_{j = 1}^{N_{d}}{{P\left( {i,j} \right)}i^{2}j^{2}}}\end{matrix}}{N_{z}}$ LDHGLE (Large Dependence High Gray LevelEmphasis): Measures the joint distribution of large dependence withhigher gray-level values.

Examples

Methods

A two-arm study, designed to explore the diagnostic and prognostic valueof coronary PVR radiomic phenotyping on CCTA was performed. The studyflowchart and baseline characteristics of the study Arms 1 and 2 arepresented in FIG. 1 and Tables 4A, 4B and 5. The research protocol wasapproved by all local institutional review boards.

Arm 1

This was a case-control study of patients with versus without adverseevents within five years after clinically-indicated assessment by CCTA.Eligible cases were retrieved from the prospectively collected data oftwo independent cohorts of patients undergoing clinically-indicatedCCTA. Out of a total of 4239 individual scans reviewed (2246 in Cohort 1and 1993 in Cohort 2), 3912 were of adequate quality and were includedin further analysis. Cases were identified based on the primarycomposite endpoint of major adverse cardiovascular events (MACE),defined as the composite of all-cause mortality and non-fatal myocardialinfarction (MI) within five years following the CCTA, whereas controlswere identified as patients with event-free follow-up for at least fiveyears post-CCTA. Following review of the quality of the scans andretrieval of relevant demographics, 1:1 matching was performed using anautomated algorithm for age, sex, obesity status, cohort and technicalparameters related to CCTA acquisition (tube voltage and CT scannerused). Where possible patients were also matched for othercardiovascular risk factors, including hypertension, dyslipidemia,diabetes mellitus and smoking. A subgroup of patients with acardiac-specific MACE (cMACE; cardiac mortality and non-fatal MI) andtheir matched controls were also examined separately to increase thesensitivity for cardiac-specific high-risk PVR features.

TABLE 4A Study Arm 1 demographics Cohort 1 MACE no MACE P value Total n83   83   — Age (years)  58.1 ± 14.9  56.7 ± 14.6 0.52 Sex (% male) 60.260.2 1.00 Hypertension (%)* 63.9 74.7 0.13 Dyslipidemia (%)* 57.8 60.20.75 Diabetes mellitus (%)* 25.3 14.5 0.08 Smoking (%)* 37/83 26/83 0.08Body Mass Index (BMI, kg/m²) 29.7 ± 8.8 30.1 ± 6.5 0.75 EAT volume (cm3)104.1 ± 60.7 101.9 ± 53.5 0.80 Medications (%)* Antiplatelets 30.1 55.40.34 Statins 56.7 41.0 0.044 ACEi/ARBs 38.6 39.8 0.98 Beta-blockers 24.115.7 0.17 Tube voltage (%) 120 kVp 75.9 75.9 1.00 100 kVp 24.1 24.1Scanner (%) 2 × 192 Somatom Force 13.3 13.3 1 × 256 Brilliance iCT 86.786.7 1.00 2 × 128 Definition Flash — — 2 × 64 Definition Flash — — 1 ×64 Sensation 64 — — CAD (%)* None to mild (0-24%) 59.4 38.6 0.01 Mild(25-49%) 42.2 44.6 Moderate (50-69%) 24.1 15.7 Severe (≥70%) 10.8  1.2High-risk plaque present 38.6 39.8 0.87 Coronary calcification (>0) 65.141.0 0.002 Values presented as percentages (%) or mean ± standarddeviation. *presented as valid percentages. ACEi: angiotensin-convertingenzyme inhibitors; ARBs: angiotensin II-receptor blockers; CAD: coronaryartery disease; (c)MACE: (cardiac-specific) major adverse cardiovascularevents.

TABLE 4B Study Arm 1 demographics Cohort 2 MACE no MACE P value Total n110   110   — Age (years)  68.0 ± 11.5  66.2 ± 11.1 0.25 Sex (% male)58.2 58.2 1.00 Hypertension (%)* 74.0 73.3 0.54 Dyslipidemia (%)* 47.352.0 0.49 Diabetes mellitus (%)* 15.8 13.9 0.41 Smoking (%)*  8.3  7.90.54 Body Mass Index (BMI, kg/m²) 28.1 ± 5.9 28.6 ± 5.6 0.66 EAT volume(cm³) 106.7 ± 57.7 107.6 ± 54.0 0.91 Medications (%)* Antiplatelets 42.4 0.5 0.54 Statins 40.7 46.8 0.60 ACEi/ARBs 56.4 56.4 0.89 Beta-blockers50.5 45.7 0.69 Tube voltage (%) 120 kVp 81.8 81.8 1.00 100 kVp 18.2 18.2Scanner (%) 2 × 192 Somatom Force — — 1 × 256 Brilliance iCT — — 1.00 2× 128 Definition Flash   0.009   0.009 2 × 64 Definition Flash   0.891  0.891 1 × 64 Sensation 64  0.1  0.1 CAD (%)* None to mild (0-24%) 21.827.3  0.021 Mild (25-49%) 33.6 46.4 Moderate (50-69%) 14.5 12.7 Severe(≥70%)  0.3 13.6 High-risk plaque present 21.8  0.2 0.74 Coronarycalcification (>0) 74.5 63.6 0.08 Values presented as percentages (%) ormean ± standard deviation. *presented as valid percentages. ACEi:angiotensin-converting enzyme inhibitors; ARBs: angiotensin II-receptorblockers; CAD: coronary artery disease; (c)MACE: (cardiac-specific)major adverse cardiovascular events.

Arm 2

This was a prospective study (Ox-IMPACT study, ethical approval providedby South-Central, Oxford C Research Ethics Committee; REC Reference17/SC/0058) that recruited 22 patients (n=22 unstable lesions)presenting with acute myocardial infarction, who were invited to undergoa series of CCTA scans within 96 hours of admission and six monthslater. A control group of 32 patients with known stable CAD (n=39 stablelesions) and previous percutaneous coronary intervention (PCI) at leastthree months before the CCTA scan were also included in this arm.Radiomic phenotypic of a coronary PVR was performed around both stableand unstable lesions to identify a radiomic signature of a PVR linked toplaque instability and inflammation.

TABLE 5 Study Arm 2 demographics Arm 3 (ACS) Arm 3 (Stable CAD) Totalsubjects included 22 32   Age (years) 53.5 [34-79] 59 [26-76] Malegender (%) 81.3 81.0 Hypertension 31.3 71.4 Dyslipidemia 31.3 76.2Diabetes Mellitus 25 23.8 Active/past smoking 25/43.8 9.1/27.3Antiplatelets 100 95.5 (aspirin/clopidogrel) Statins 93.8 85.7 ACEi orARBs 87.5 63.6 Beta-blockers 93.8 76.2 Values presented as median[range] or percentages (%); ACEi: Angiotensin-Converting Enzymeinhibitors; ACS: acute coronary syndromes; ARBs: Angiotensin-II-ReceptorBlockers; CAD: coronary artery disease.

Radiomic Features Included in Study

A total of 843 PVR radiomic features were measured, as summarized inTable 6.

TABLE 6 Breakdown of PVR radiomic features Wavelet transformationsOriginal (n = 8) All First order 18 144 162 Shape-related 15 — 15 GLCM23 184 207 GLDM 14 112 126 GLRLM 16 128 144 GLSZM 16 128 144 NGTDM 5 4045 Total 107 736 843 GLCM: gray level co-occurrence matrix; GLDM: graylevel dependence matrix; GLRLM: gray level run length matrix; GLSZM:gray level size zone matrix; NGTDM: neighbouring gray tone dependencematrix; PVR: perivascular region.

Data Collection, Definitions and Outcome Assessment

In Arm 1, outcome data were assembled through search of medical records,and querying of local/national databases by local investigators notinvolved in subsequent image/data analysis. Appropriate institutionalreview board approval was obtained with waiver of individual informedconsent. Clinical data and demographics were recorded prospectively inthe electronic medical records at the time of initial clinical encounterand manually extracted for the current study. Hypertension was definedbased on the presence of a documented diagnosis or treatment with anantihypertensive regimen, according to the relevant clinical guidelines(James P A, Oparil S, Carter B L, et al. 2014 evidence-based guidelinefor the management of high blood pressure in adults: report from thepanel members appointed to the Eighth Joint National Committee (JNC 8).JAMA 2014; 311(5): 507-20). Similar criteria were applied for thedefinition of hypercholesterolemia and diabetes mellitus (AmericanDiabetes A. Diagnosis and classification of diabetes mellitus. DiabetesCare 2014; 37 Suppl 1: S81-90; Stone N J, Robinson J G, Lichtenstein AH, et al. 2013 ACC/AHA guideline on the treatment of blood cholesterolto reduce atherosclerotic cardiovascular risk in adults: a report of theAmerican College of Cardiology/American Heart Association Task Force onPractice Guidelines. J Am Coll Cardiol 2014; 63(25 Pt B): 2889-934).Ascertainment of the exact cause of death was performed locally by studyinvestigators at each site, through chart review, inspection of thedeath certificate and/or telephone follow-up and/or verification with afamily member. Cardiac and non-cardiac mortality were defined accordingto the recommendations of the ACC/AHA and the Academic ResearchConsortium, as described previously. More specifically, cardiacmortality was defined as any death due to proximate cardiac causes (e.g.myocardial infarction, low-output heart failure, fatal arrhythmia).Deaths fulfilling the criteria of sudden cardiac death were alsoincluded in this group. Any death not covered by the previousdefinition, such as death caused by malignancy, accident, infection,sepsis, renal failure, suicide or other non-cardiac vascular causes suchas stroke or pulmonary embolism was classified as non-cardiac. Deathswhere information on the cause of death could not be collected withcertainty were classified as “deaths of unknown cause” at the discretionof the local site investigators. Non-fatal myocardial infarction eventsduring follow-up (ST-segment elevation or non-ST segment elevation) werealso retrieved through search of electronic health records.

Coronary CT Angiography (CCTA) Acquisition Protocol

Cohort 1:

The majority of the CCTA scans (87.1%) were performed on a 256-sliceBrilliance iCT scanner (Philips Medical Systems, Best, The Netherlands),with the remainder using a 2×128-slice Definition Flash scanner (SiemensHealthcare, Erlangen, Germany) (10.8%) and a 2×192-slice Somatom ForceCT scanner (Siemens Healthcare, Forchheim, Germany) (2.1%). In patientswith heart rate >60 beats/minute, 5 mg of intravenous metoprolol (withincremental 5 mg doses up to a maximum dose of 30 mg) or intravenousdiltiazem (5 mg increments up to 20 mg maximum), if the heart rateremained above 60 beats per minute once the patient was positioned onthe CT table. Patients also received 0.3 mg of nitroglycerinsublingually immediately before CCTA and iodinated contrast (Omnipaque350, General Electric, Milwaukee, USA) was administered at flow rate of5-6 ml/s.

Cohort 2:

CCTA scans were performed on a 2×64-slice scanner (Definition Flash,Siemens Healthcare, Forchheim, Germany) (79.2%), with the remainderusing either a 64-slice (Siemens Sensation 64, Siemens Healthcare,Forchheim, Germany) (18.1%) or 2×128-slice scanner (2.7%) (SomatomDefinition Flash, Siemens Healthcare, Forchheim, Germany). Oralmedication with 100 mg atenolol was administered one hour before CT ifheart rate was >60 beats per minute with additional 5 mg doses ofmetoprolol intravenously up to a maximum dose of 30 mg, if the heartrate remained above 60 beats per minute once the patient was positionedon the CT table. Patients also received 0.8 mg of nitroglycerinesublingually immediately before CCTA and iodinated contrast (Omnipaque350, Schering AG, Berlin, Germany) was administered at flow rate of 5-6ml/s.

Study Arm 2:

Participants in Study Arm 2 underwent CCTA using a 64-slice scanner(General Electric, LightSpeed Ultra, General Electric, Milwaukee, Wis.,USA). Heart rate was optimised using intravenous injection ofbeta-blockers and sublingual glyceryl-trinitrate (800 μg) was alsoadministered to achieve maximum coronary vasodilatation. CCTA wasperformed following intravenous injection of 95 ml of iodine basedcontrast medium (Niopam 370, BRACCO UK Ltd) at a flow rate of 6 mL/sec(tube energy of 120 kVp, axial slice thickness of 0.625 mm, rotationtime of 0.35 sec, detector coverage of 40 mm). Prospective imageacquisition was used by ECG-gating at 75% of cardiac cycle (with 100msec padding for optimal imaging of the right coronary artery ifrequired).

CCTA Scan Processing and Analysis

All images were first anonymized locally, and subsequently transferredto a core lab (Academic Cardiovascular CT Unit, University of Oxford,United Kingdom) for analysis on a dedicated workstation (AquariusWorkstation® V.4.4.13, TeraRecon Inc., Foster City, Calif., USA) byinvestigators blinded to population demographics and outcomes. All scanswere initially reviewed based on their quality and presence of artefactsprecluding a reliable qualitative and quantitative evaluation.Low-quality scans were reviewed by at least two independentinvestigators before being excluded from subsequent analysis. Mild,moderate and severe coronary stenoses were defined as luminal stenosis25-49%, 50-69% and ≥70%, respectively (as previously described in Cury RC, Abbara S, Achenbach S, et al. CAD-RADS™ Coronary ArteryDisease—Reporting and Data System. An expert consensus document of theSociety of Cardiovascular Computed Tomography (SCCT), the AmericanCollege of Radiology (ACR) and the North American Society forCardiovascular Imaging (NASCI). Endorsed by the American College ofCardiology. J Cardiovasc Comput Tomogr 2016; 10(4): 269-81). Obstructivecoronary artery disease (CAD) was defined as the presence of ≥1 coronarylesion causing luminal stenosis ≥50%, whereas CAD extent was assessed bythe Duke Prognostic CAD Index (for example, as defined in Min J K, ShawL J, Devereux R B, et al. Prognostic value of multidetector coronarycomputed tomographic angiography for prediction of all-cause mortality.J Am Coll Cardiol 2007; 50(12): 1161-70). High-risk plaque features weredefined as the presence of at least one of the following features onCCTA: a) spotty-calcification, b) low-attenuation plaque, c) positiveremodeling and d) napkin-ring sign (as previously described in Puchner SB, Liu T, Mayrhofer T, et al. High-risk plaque detected on coronary CTangiography predicts acute coronary syndromes independent of significantstenosis in acute chest pain: results from the ROMICAT-II trial. J AmColl Cardiol 2014; 64(7): 684-92). Epicardial (visceral) obesity wasassessed by measuring the total epicardial adipose tissue (EAT) volumein a semi-automated manner by tracking the contour of the pericardiumfrom the level of the pulmonary artery bifurcation to the apex of theheart at the most caudal end. FAI_(PVAT) was defined as previouslydescribed in Antonopoulos A S, Sanna F, Sabharwal N, et al. Detectinghuman coronary inflammation by imaging perivascular fat. Sci Transl Med2017; 9(398).

Coronary PVR Radiomic Feature Extraction

Calculation of radiomic features in a coronary PVR was performed in allselected CCTA scans using 3D Slicer (v.4.9.0-2017-12-18 r26813,available at http://www.slicer.org). To avoid issues of collinearitybetween different coronary vessels, analysis in Arm 1 was restricted tothe proximal and mid right coronary artery (RCA) (segments 1 and 2according to the anatomical classification of the American HeartAssociation). The coronary PVR was defined as all voxels in theHounsfield Unit range of −190 to −30 Hounsfield Units (HU) locatedwithin a radial distance from the outer vessel wall equal to thediameter of the adjacent vessel. Segmentation of the coronary PVR wasperformed by placing a three-dimensional sphere with a diameter equal tothree times the diameter of the coronary vessel on consecutive slicesfollowing the centerline of the vessel. The segmented PVR wassubsequently extracted and used to calculate radiomic features, usingthe SlicerRadiomics extension of 3D Slicer, which incorporates thePyradiomics library into 3D Slicer. Shape-related and first-orderradiomic features were calculated using the raw HU values of thesegmented PVR. For calculation of texture features (Gray LevelCo-occurrence Matrix [GLCM], Gray Level Dependence Matrix [GLDM], GrayLevel Run-Length Matrix [GLRLM], Gray Level Size Zone Matrix [GLSZM],and Neighbouring Gray Tone Difference Matrix [NGTDM], FIG. 1A, TablesR1-R7), the PVR voxels were discretized into 16 bins of equal width(width of ten HU), to reduce noise while allowing a sufficientresolution to detect biologically significant spatial changes in the PVRattenuation. To enforce symmetrical, rotationally-invariant results,texture statistics (GLCM etc) were calculated in all four directions andthen averaged (for example, as previously described in Kolossvary M,Kellermayer M, Merkely B, Maurovich-Horvat P. Cardiac ComputedTomography Radiomics: A Comprehensive Review on Radiomic Techniques.Journal of thoracic imaging 2018; 33(1): 26-34).

Wavelet Transformation:

First order and texture-based statistics were also calculated forthree-dimensional wavelet transformations of the original imageresulting in eight additional sets of radiomic features (FIG. 1A).

Statistical Analysis

In Arm 1, the case-control matching was performed using an automatedalgorithm, provided by the ccmatch command in Stata. In the final studypopulation, clinical demographics are presented as mean±standarddeviation for continuous variables, and percentages for categoricalvariables. Continuous variables between two groups were compared byStudent's t-test, whereas categorical variables are compared usingPearson's Chi-square test.

Principal Components and Unsupervised Clustering:

In both Study Arms, all 843 calculated PVR radiomic features wereincluded in principal component analysis to identify principalcomponents that describe most of the phenotypic variation in the studypopulation. The three first components in Arm 1 (PC1, PC2, PC3) and Arm2 (PC1′, PC2′ and PC3′) were then used to perform hierarchicalclustering of the observations (using the Ward method and the Minkowskidistance). The frequency of MACE (Arm 1) and unstable plaques (Arm 2)between distinct clusters were compared by a Chi-square test.

Feature Selection and Improved Discrimination:

First, the discriminatory value of all radiomic features for 5-year MACEwas tested in receiver operating characteristic curve (ROC) analysis.This analysis was performed on pooled data for both Cohorts. To correctfor multiple comparisons, a genome-wide association study (GWAS)-basedapproach that has been previously used in the field of radiomic imageanalysis was followed, by applying a Bonferroni correction for thenumber of principal components which account for 99.5% of thevariability in our study sample (see, for example, Kolossvary M, KaradyJ, Szilveszter B, et al. Radiomic Features Are Superior to ConventionalQuantitative Computed Tomographic Metrics to Identify Coronary PlaquesWith Napkin-Ring Sign. Circ Cardiovasc Imaging 2017; 10(12) and JohnsonR C, Nelson G W, Troyer J L, et al. Accounting for multiple comparisonsin a genome-wide association study (GWAS). BMC Genomics 2010; 11: 724).Bivariate associations between radiomic features were assessed by thenon-parametric Spearman's rho (ρ) coefficient, whereas intra-observervariability was assessed in ten scans by means of the intraclasscorrelation coefficient (ICC).

In order to build a radiomic signature of high-risk PVR, a multi-stepapproach was followed. Z-score transformation was applied to allfeatures and unstable radiomic features with low ICC in repeatedanalysis (<0.9) were excluded. To minimize false positive findingsdriven by cohort-specific variations, we then selected features thatwere significantly associated with MACE in both cohorts (at the level ofα=0.05). Next, collinearity was reduced by stepwise removal of pairwisecomparisons using an appropriate function of the caret package on R. Amachine learning approach was then applied in Cohort 1 using elasticnetwork regression and leave-one-out internal cross-validation. Theoptimal penalty coefficient (lambda, λ) was selected bycross-validation, while alpha was set at α=1. The best performing modelsfor both MACE and cMACE were then validated externally in Cohort 2, anddiscrimination was assessed by calculating the Area Under the Curve(AUC). The top variables of the best performing model were then combinedin a unified score/signature by multiplying each one by the respectiveunadjusted beta coefficients of the model and calculating the total sum.The unified signature was then added in a logistic regression modelconsisting of the following four blocks: i) age, sex, hypertension,dyslipidemia, smoking and diabetes mellitus (Model 1); ii) Model1+CT-derived measurements, including Duke Prognostic CAD index, presenceof high-risk plaque features, EAT volume and presence of coronarycalcium (Model 2); iii) Model 2+FAI_(PVAT) (Model 3); and iv) Model3+PVR texture signature. The prognostic value of the nested models forMACE and cMACE was compared by means of their respective C-statistics(Area Under the Curve, AUC). The interaction between FAI_(PVAT) and thePVR texture signature is presented graphically using two-way contourplots derived from the previous multiple logistic regression models.Comparison of the selected radiomic features between unstable and stableplaques in Arm 2 was performed using the non-parametric Mann-Whitneytest. Statistical analyses were performed in the R environment(packages: caret, hclust), as well as Stata v14.0 (Stata Corp Inc.,College Station, Tex.). All tests were two-sided and a was set at 0.05,unless specified otherwise.

Results

Study Population Demographics

Out of 3912 individual scans that were reviewed in Arm 1, a total of 386scans were included in the study, corresponding to 193 patients with5-year MACE and 193 matched controls. A selected subgroup of 98 patientswith cardiac-specific mace (cMACE) and their matched controls were alsoidentified and analysed in a subgroup-type analysis. The populationdemographics and baseline characteristics of the study Arm 1 populationare summarized in Tables 4A and 4B. Cases and controls were notsignificantly different in terms of their baseline demographics,however, as expected, cases (MACE or cMACE) were more likely to havecoronary artery disease (CAD), as assessed by the degree of coronarystenosis and the Duke Prognostic CAD index) compared to their controls.Study Arm 2 included 22 patients with unstable lesions, and 32 age- andsex-matched controls with a total of 39 stable lesions (Table 5).

PVR Radiomics: Component Analysis and Association with Adverse Events

A total of 103 radiomic features were calculated from the originalimages, corresponding to 15 shape-related features in addition to 18first order statistics, 23 GLCM, 14 GLDM, 16 GLRLM, 16 GLSZ and 5 NGTDMindividual features (Table 6, FIG. 4). All features, except for theshape-related features, were also calculated for each one of the eightwavelet transformation of the segmented region, resulting in a total of843 radiomic features. Principal component analysis of all radiomicfeatures revealed three principal components that accounted for 61.98%of the observed variation in both cohorts of Arm 1 (FIG. 5A), while 92components accounted for 99.5% of the variation in the study population(scree plot presented in FIG. 5B). Out of 42 components witheigenvalues >1, a total of six components were significant predictors ofMACE (FIG. 5C), while four components remained independently associatedwith MACE in a multiple regression model including all five componentsadjusted for age, sex, cardiovascular risk factors and CCTA-derivedindices of CAD extent (FIG. 5D). These components were differentiallyassociated with baseline clinical demographics and characteristics (FIG.5E), possibly reflecting features of PVR that described distinctbiological phenotypes. Of note, inclusion of the four PVR components ina model that included age, sex, cardiovascular risk factors andCCTA-derived risk features significantly improved discrimination for5-year MACE (FIG. 5F), suggesting that radiomic phenotyping of PVRcarries a strong and incremental prognostic value.

Unsupervised Clustering Based on Coronary PVR Phenotyping

Unsupervised (hierarchical) clustering of the pooled Arm 1 studypopulation using the first three principal components of coronary PVRradiomics (PC1, PC2 and PC3) identified three distinct clusters withsignificantly different risk of 5-year MACE (46.5% vs 45.8% vs 65.8%MACE, P=0.009). Similarly, in Arm 2, hierarchical clustering of theidentified coronary lesions, identified two distinct clusters withsignificant different prevalence of unstable plaques (58.8% vs 25%,P=0.01). These findings suggest the presence of a distinctive radiomicsignature in PVR linked to increased cardiovascular disease and thelocal presence of coronary inflammation and unstable lesions.

Identifying Specific High-Risk PVR Radiomic Features

Principal component analysis and unsupervised clustering proved theconcept that radiomic phenotyping of PVR can be linked to both localpresence of coronary inflammation/disease and worse outcomes. However,they fail to identify specific high-risk radiomic features that can bereproducibly measured in independent cohorts.

Principal components are specific to the dataset from which they werederived and are not easily applicable to independent datasets andcohorts. Further work was therefore undertaken to identify specificfeatures that can supplement the diagnostic and prognostic informationof the established FAI_(PVAT) marker. In ROC analysis for discriminationof the primary endpoint of MACE, a total of 198 features were found tobe significant at the level of 0.05 using the pooled data for bothcohorts. In order to correct for multiple comparisons and decrease thefalse discovery rate (FDR), a Bonferroni correction was applied based onthe principal component analysis (new significancecutoff=0.05/92=0.00054347826). Following this correction, only 46radiomic features remained significant discriminators of MACE, assummarized in a

Manhattan plot (FIG. 6) and in Table 3. Of these 46 radiomic features,28 were first order statistics, 10 GLRLM, 5 GLCM, 1 GLDM, 1 GLSZ and 1NGTDM, while half were derived from the original image and the otherhalf from wavelet transformation (17 LLL, 2 HHH, 3 HHL and 1 LHL).

Building a High-Risk PVR Radiomic Signature

While individual radiomic features such as FAI_(PVAT) are associatedwith an increased cardiovascular risk, it was previously unknown whethera combination (“signature”) of different radiomic features may provide amore powerful way to characterize the adverse profile of coronary PVR.To explore this hypothesis and develop a radiomic signature that wouldbe both prognostic and reproducible, a stringent, stepwise approach wasapplied (FIG. 2). First, out of the 843 coronary PVR radiomic featuresthat were calculated, 143 were excluded following stability analysis(ICC<0.9, two measurements) (FIG. 7). Next, 60 volume- andorientation-independent radiomic features that were significantlyassociated with MACE at the level of α=0.05 in both cohorts wereselected, in order to reduce possible false positive findings due tocohort-specific variations. Collinearity was subsequently reduced bystepwise elimination of pairwise correlations at the level of |rho|≥0.75(Spearman's rho). Using the remaining nine radiomic features, a machinelearning approach was applied in Cohort 1 using elastic net/lassoregression and leave-one-out internal cross-validation. The bestperforming model for prediction of MACE showed average discrimination(FIG. 2B), and a similar model for prediction of cardiac-specific MACE(FIG. 2C) showed very good discriminatory value in both Cohort 1(derivation) and Cohort 2 (validation cohort). The top six components ofthis model were then used to define the Perivascular Texture Index (PTI)using the model-derived coefficients, as shown in Table 7. Table 7therefore describes a particular example of the radiomic signature ofthe invention.

TABLE 7 Defining the high-risk PVR texture signature PVR radiomicRadiomic feature z-score betas unstand. Betas feature (rf_(i)) group(b_(z)) (b_(i)) SRHGLE GLRLM 4.0689831 0.257217 Skewness First Order2.4393009 8.721041 Run Entropy GLRLM 1.5392412 7.914576 SALGLE Firstorder 1.0821666 141.4015 Zone Entropy (HHH) GLSZM −0.5023836 −0.85001Zone Entropy GLSZM 0.8234266 3.504424 Perivascular Texture Index (PTI) =90 − Σb_(i) rf_(i) GLRLM: gray level run length matrix; GLSZM: graylevel size zone matrix; PVR: perivascular region; SRHGLE: Short Run HighGray Level Emphasis; SALGLE: small area low gray level emphasis; SZNU:size zone nonuniformity.

In Table 7, z-score betas were converted to unstandardized betas (b₁) bymultiplying b_(z) by the standard deviation of the respective variablein the derivation cohort (Cohort 1). A constant of 90 was added post-hocto ensure positive values based on the range of values observed in allcohorts that were analysed.

Incremental Value of PVR Radiomic Phenotyping Beyond CurrentState-of-the-Art

To assess the incremental value of FAI_(PVAT) radiomic phenotypingbeyond current risk biomarkers used in CCTA-based risk stratification, aset of nested models were constructed, as shown in FIGS. 3A and 3B.Model 1 consisted of demographics and conventional risk factors, whichshowed poor discrimination for both MACE and cMACE in part due to thematching process for the selection of the control group. Addition ofCCTA-derived risk features (including Duke Prognostic CAD index,presence of coronary calcium, high-risk plaque features, and EAT(epicardial adipose tissue) volume) significantly improveddiscrimination for both MACE and cMACE, while inclusion of FAI_(PVAT)further increased discrimination for both endpoints. Despite thisremarkable improvement, the addition of PTI (as defined in Table 7) wasassociated with a further significant improvement in the discriminatoryvalue of the model for both endpoints (FIGS. 3A and 3B), suggesting notonly an independent but also an incremental value for PVR texturephenotyping in risk prediction. The interaction between FAI_(PVAT) andPTI for prediction of MACE/cMACE is graphically presented in FIG. 3C,which demonstrates that for a given FAI_(PVAT) value, there is anincreasing risk at higher levels of PTI and vice versa.

Validating Alternative Radiomic Signatures (PTIs) of the Invention

The data presented in FIGS. 3A and 3B demonstrate that the radiomicsignature (PTI) defined in Table 7 provides a significant improvement inthe discriminatory value of the model for both endpoints (MACE andcMACE). To validate the usefulness of alternative radiomic signatures ofthe invention that include different selections of radiomic features, aseries of models including several different radiomic signatures weretested against a current state of the art model.

In Table 8, improvements in model performance are presented in 196patients (98 with cardiac MACE and 98 matched controls). Each stepcorresponds to inclusion of one selected radiomic feature on top of thecurrent state-of-the-art model and radiomic features of previousclusters. The current state-of-the-art model includes age, sex,hypertension, dyslipidemia, smoking and diabetes mellitus, DukePrognostic Coronary Artery Disease index, presence of high-risk plaquefeatures, epicardial adipose tissue volume and presence of coronarycalcium.

In each of Examples 1-4, the current state of the art model wasprogressively supplemented by a radiomic signature includingprogressively more radiomic features from different clusters. First, thestate of the art model was supplemented by a radiomic signaturecalculated on the basis of a radiomic feature selected from cluster 1(first row of Tables 8A and 8B: “+Cluster 1”). Next, the state of theart model was supplemented by a radiomic signature calculated on thebasis of two radiomic features selected from clusters 1 and 2 (first rowof Tables 8A and 8B: “+Cluster 2”). Thus, each progressive row of Tables8A and 8B corresponds to the inclusion of one selected radiomic featureon top of the current state-of-the-art model and the radiomic featuresof previous clusters. Nagelkerke's pseudo-R² provides a measure of thediscrimination of the model for cMACE.

It can clearly be seen from Tables 8A and 8B that the signatures of theinvention calculated on the basis of different selections of radiomicfeatures from the identified clusters all provide improved predictionfor cardiac-specific MACE. Thus, the data presented in Table 8demonstrate that regardless of which features are selected from each ofthe identified clusters, or precisely how many are selected, theradiomic signature (PTI) of the invention provides improved predictionof cardiovascular risk over previously used models.

TABLE 8A Improved prediction for cardiac-specific MACE with differentselections of radiomic features from the identified clusters Example 1:Example 2: “Original” Nagelkerke's Top alternative Nagelkerke's radiomicpseudo-R² feature from each pseudo-R² features (delta from cluster ofTable 2 (delta from (Table 1) previous step) (expanded clusters)previous step) Current state-of-the-art* 0.110 (—)     — 0.110 (—)    +Cluster 1 Short Run High 0.174 (+0.064) High Gray Level 0.179 (+0.069)Gray Level Emphasis Emphasis +Cluster 2 Skewness 0.211 (+0.037) SkewnessLLL 0.205 (+0.026) +Cluster 3 Run Entropy 0.229 (+0.018) DependenceEntropy LLL 0.214 (+0.009) +Cluster 4 Small Area Low 0.252 (+0.023) LowGray Level 0.242 (+0.028) Gray Level Emphasis Zone Emphasis +Cluster 5Zone Entropy 0.295 (+0.043) Gray Level Non 0.249 (+0.007) UniformityNormalized (GLRLM) +Cluster 6 Zone Entropy HHH 0.296 (+0.001) Size ZoneNon 0.303 (+0.054) Uniformity Normalized HHH +Cluster 7 Strength 0.298(+0.002) Coarseness HLL 0.306 (+0.003) +Cluster 8 Cluster tendency LLL0.299 (+0.001) Cluster Tendency 0.309 (+0.003) +Cluster 9 Size Zone Non0.300 (+0.001) Dependence Non 0.311 (+0.002) Uniformity LLL UniformityHLL

TABLE 8B Improved prediction for cardiac-specific MACE with differentselections of radiomic features from the identified clusters Example 3:Example 4: Bottom alternative Nagelkerke's Top alternative Nagelkerke'sfeature from each pseudo-R² feature from each pseudo-R² cluster of Table2 (delta from cluster of Table 1 (delta from (expanded clusters)previous step) (standard clusters) previous step) Currentstate-of-the-art* 0.110 (—)     — 0.110 (—)     +Cluster 1 High GrayLevel 0.140 (+0.030) High Gray Level 0.179 (+0.069) Zone EmphasisEmphasis +Cluster 2 Median 0.234 (+0.094) Skewness LLL 0.205 (+0.026)+Cluster 3 Mean LLL 0.236 (+0.002) Run Entropy LLL 0.242 (+0.037)+Cluster 4 Contrast 0.237 (+0.001) Low Gray Level 0.243 (+0.001) ZoneEmphasis +Cluster 5 Uniformity 0.248 (+0.011) Zone Entropy 0.245(+0.002) +Cluster 6 Small Area 0.289 (+0.041) Zone Entropy HHH 0.284(+0.039) Emphasis HHH +Cluster 7 Coarseness LHH 0.289 (+0.000) Strength0.285 (+0.001) +Cluster 8 10th Percentile 0.297 (+0.008) ClusterTendency 0.298 (+0.013) +Cluster 9 Run Length Non 0.304 (+0.007)Busyness 0.303 (+0.005) Uniformity HHH

PVR Radiomic Phenotyping to Detect Unstable Lesions

When calculated around pre-defined coronary lesions in Study Arm 2, allbut one of the identified radiomic features used to define PTI weresignificantly altered in the presence of unstable, culprit lesions(scanned within 96 hours of ACS onset) compared to stable, treatedlesions (scanned >3 months post-PCI) (FIGS. 8A-G). More importantly, PTI(defined using the formula of Table 7) outperformed all six individualradiomic features in discriminating unstable form stable coronarylesions (AUC: 0.76; 95% confidence interval: 0.64-0.88) (FIG. 8G). Thesefindings suggest the value of perivascular fat phenotyping by means ofPTI in combination with FAI_(PVAT) for both future risk prediction anddetection of unstable coronary plaques, and reveal a close link betweenperivascular fat phenotype and vascular inflammation, plaque instabilityand adverse clinical outcomes.

Summary of Findings

Using a machine learning approach, the inventors have discovered andvalidated a coronary PVR radiomic signature that adds incremental valuebeyond traditional risk factors and established CCTA risk classificationtools in predicting future adverse events and evaluating cardiovascularhealth and risk, and further detects local plaque inflammation and thepresence of unstable coronary lesions. The inventors have demonstratedthat a PVR radiomic signature based on two or more radiomic features ofthe PVR provides a tool for predicting future adverse events inpatients, for diagnosing coronary artery disease or coronary heartdisease, and for identifying unstable coronary lesions.

The PVR signature of the invention describes the high-risk PVRphenotype, linking it to future event risk, and offers incrementalprognostic information beyond current CCTA-based tools. The signature ofthe invention is also able to discriminate unstable from stable coronarylesions based on the radiomic signature of peri-lesion fat. Takentogether, the findings presented herein demonstrate that PVR radiomicphenotyping by means of the radiomic signature of the invention can beused to identify both the high-risk patient (when measured in astandardized way around coronary vessels) and the high-risk lesion (whenapplied around a specific coronary segment or lesion) with importantimplications for modern CCTA-based risk prediction.

Surprisingly, the radiomic signature need not be constructed from theradiomic features that are most strongly independently associated withfuture adverse events. Instead, it is actually advantageous to include aselection of radiomic features from different collinear “clusters” ofradiomic features instead of merely including those radiomic featuresthat are individually most associated with adverse events.

A particularly attractive aspect of the invention is that it can beperformed on historic medical imaging data that have been collectedpreviously. The signature of the invention may be derived and calculatedbased on historic imaging data and the invention therefore provides aconvenient tool for assessing a large number of patients without theneed to perform further scans. The method of the invention need nottherefore include the step of collecting the medical imaging data andcan be performed based on a post-hoc analysis of existing medicalimaging data.

Selected Aspects of the Invention

The following numbered clauses disclose various aspects of theinvention.

Clause 1. A method for characterising a perivascular region usingmedical imaging data of a subject, the method comprising calculating thevalue of a radiomic signature of the perivascular region using themedical imaging data;

-   -   wherein the radiomic signature is calculated on the basis of        measured values of at least two radiomic features of the        perivascular region, the measured values of the at least two        radiomic features being calculated from the medical imaging        data.

Clause 2. The method of clause 1, wherein the at least two radiomicfeatures are selected from the radiomic features of clusters 1 to 9,wherein the at least two radiomic features are each selected fromdifferent clusters, wherein:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, High Gray Level Run Emphasis,        Autocorrelation, Sum Average, Joint Average, and High Gray Level        Zone Emphasis;    -   cluster 2 consists of Skewness, Skewness LLL, Kurtosis, 90th        Percentile, 90th Percentile LLL, Median LLL, Kurtosis LLL, and        Median;    -   cluster 3 consists of Run Entropy, Dependence Entropy LLL,        Dependence Entropy, Zone Entropy LLL, Run Entropy LLL, and Mean        LLL;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, Low        Gray Level Zone Emphasis, Short Run Low Gray Level Emphasis, Low        Gray Level Run Emphasis, Low Gray Level Emphasis, Small        Dependence Low Gray Level Emphasis, Gray Level Variance LLL        (GLSZM), Gray Level Variance (GLDM), Variance, Gray Level        Variance (GLDM), Difference Variance LLL, Gray Level Variance        LLL (GLRLM), Variance LLL, Gray Level Variance LLL (GLDM), Sum        of Squares, Contrast LLL, Mean Absolute Deviation, Interquartile        Range, Robust Mean Absolute Deviation, Long Run Low Gray Level        Emphasis, Difference Variance, Gray Level Variance (GLSZM),        Inverse Difference Moment Normalized, Mean Absolute Deviation        LLL, Sum of Squares LLL, and Contrast;    -   cluster 5 consists of Zone Entropy, Gray Level Non Uniformity        Normalized (GLRLM), Gray Level Non Uniformity Normalized LLL        (GLRLM), Sum Entropy, Joint Energy, Entropy, Gray Level Non        Uniformity Normalized (GLDM), Joint Energy, Gray Level Non        Uniformity Normalized LLL (GLDM), Uniformity LLL, Sum Entropy        LLL, and Uniformity;    -   cluster 6 consists of Zone Entropy HHH, Size Zone Non Uniformity        Normalized HHH, and Small Area Emphasis HHH;    -   cluster 7 consists of Strength, Coarseness HLL, Coarseness,        Coarseness LHL, Coarseness LLL, Coarseness LLH, Coarseness HHH,        Coarseness HLH, Coarseness HHL, and Coarseness LHH;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, Sum Entropy,        Interquartile Range, Cluster Prominence LLL, Entropy LLL, 10th        Percentile LLL, 10th Percentile; and    -   cluster 9 consists of Size Zone Non Uniformity LLL, Dependence        Non Uniformity HLL, Gray Level Non Uniformity HLL (GLSZM), Gray        Level Non

Uniformity (GLSZM), Run Length Non Uniformity HHL, Run Length NonUniformity LHL, Dependence Non Uniformity LHL, Dependence NonUniformity, Run Length Non Uniformity HLH, Busyness, Run Length NonUniformity LLH, Dependence Non Uniformity LLH, Dependence Non UniformityLLL, Size Zone Non Uniformity, Energy HLL, Run Length Non UniformityLHH, Size Zone Non Uniformity HLL, Gray Level Non Uniformity LLH(GLSZM), Gray Level Non Uniformity LHL (GLSZM), Gray Level NonUniformity LLL (GLSZM), Run Length Non Uniformity HLL, Gray Level NonUniformity HLH (GLSZM), Gray Level Non Uniformity HHL (GLSZM), RunLength Non Uniformity, and Run Length Non Uniformity HHH.

Clause 3. The method of clause 2, wherein:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, High Gray Level Run Emphasis,        Autocorrelation, Sum Average, and Joint Average;    -   cluster 2 consists of Skewness, Skewness LLL, Kurtosis, 90th        Percentile, 90th Percentile LLL, Median LLL, and Kurtosis LLL;    -   cluster 3 consists of Run Entropy, Dependence Entropy LLL,        Dependence Entropy, and Zone Entropy LLL;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, Low        Gray Level Zone Emphasis, Short Run Low Gray Level Emphasis, Low        Gray Level Run Emphasis, Low Gray Level Emphasis, Small        Dependence Low Gray Level Emphasis, Gray Level Variance LLL        (GLSZM), Gray Level Variance (GLDM), Variance, Gray Level        Variance (GLDM), and Difference Variance LLL;    -   cluster 5 consists of Zone Entropy, Gray Level Non Uniformity        Normalized (GLRLM), and Gray Level Non Uniformity Normalized LLL        (GLRLM);    -   cluster 6 consists of Zone Entropy HHH, and Size Zone Non        Uniformity Normalized HHH;    -   cluster 7 consists of Strength, Coarseness HLL, Coarseness,        Coarseness LHL, Coarseness LLL, Coarseness LLH, and Coarseness        HHH;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, Sum Entropy,        Interquartile Range, Cluster Prominence LLL, Entropy LLL, 10th        Percentile LLL, and 10th Percentile; and    -   cluster 9 consists of Size Zone Non Uniformity LLL, Dependence        Non Uniformity HLL, Gray Level Non Uniformity HLL (GLSZM), Gray        Level Non Uniformity (GLSZM), Run Length Non Uniformity HHL, Run        Length Non Uniformity LHL, Dependence Non Uniformity LHL,        Dependence Non Uniformity, Run Length Non Uniformity HLH,        Busyness, Run Length Non Uniformity LLH, Dependence Non        Uniformity LLH, Dependence Non Uniformity LLL, Size Zone Non        Uniformity, Energy HLL, Run Length Non Uniformity LHH, Size Zone        Non Uniformity HLL, Gray Level Non Uniformity LLH (GLSZM), and        Gray Level Non Uniformity LHL (GLSZM).

Clause 4. The method of clause 2, wherein:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, High Gray Level Run Emphasis,        Autocorrelation, Sum Average, and Joint Average;    -   cluster 2 consists of Skewness, Skewness LLL, Kurtosis, and 90th        Percentile;    -   cluster 3 consists of Run Entropy, Dependence Entropy LLL, and        Dependence Entropy;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, Low        Gray Level Zone Emphasis, Short Run Low Gray Level Emphasis, Low        Gray Level Run Emphasis, Low Gray Level Emphasis, and Small        Dependence Low Gray Level Emphasis;    -   cluster 5 consists of Zone Entropy, and Gray Level Non        Uniformity Normalized (GLRLM);    -   cluster 6 consists of Zone Entropy HHH;    -   cluster 7 consists of Strength, Coarseness HLL, Coarseness,        Coarseness LHL, Coarseness LLL, and Coarseness LLH;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, Sum Entropy,        Interquartile Range, Cluster Prominence LLL, Entropy LLL, 10th        Percentile LLL, and 10th Percentile; and    -   cluster 9 consists of Size Zone Non Uniformity LLL, Dependence        Non Uniformity HLL, Gray Level Non Uniformity HLL (GLSZM), Gray        Level Non Uniformity (GLSZM), Run Length Non Uniformity HHL, Run        Length Non Uniformity LHL, Dependence Non Uniformity LHL,        Dependence Non Uniformity, Run Length

Non Uniformity HLH, Busyness, Run Length Non Uniformity LLH, DependenceNon Uniformity LLH, Dependence Non Uniformity LLL, and Size Zone NonUniformity.

Clause 5. The method of clause 2, wherein:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, High Gray Level Run Emphasis, and        Autocorrelation;    -   cluster 2 consists of Skewness, and Skewness LLL;    -   cluster 3 consists of Run Entropy, and Dependence Entropy LLL;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, and        Low Gray Level Zone Emphasis;    -   cluster 5 consists of Zone Entropy;    -   cluster 6 consists of Zone Entropy HHH;    -   cluster 7 consists of Strength;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, Sum Entropy,        Interquartile Range, Cluster Prominence LLL, Entropy LLL, 10th        Percentile LLL, and 10th Percentile; and    -   cluster 9 consists of Size Zone Non Uniformity LLL, Dependence        Non Uniformity HLL, Gray Level Non Uniformity HLL (GLSZM), Gray        Level Non Uniformity (GLSZM), Run Length Non Uniformity HHL, and        Run Length Non Uniformity LHL.

Clause 6. The method of clause 2, wherein:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, and High Gray Level Run Emphasis;    -   cluster 2 consists of Skewness, and Skewness LLL;    -   cluster 3 consists of Run Entropy;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, and        Low Gray Level Zone Emphasis;    -   cluster 5 consists of Zone Entropy;    -   cluster 6 consists of Zone Entropy HHH;    -   cluster 7 consists of Strength;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Sum of Squares LLL, Mean Absolute Deviation LLL, Gray Level        Variance LLL (GLDM), Variance LLL, Gray Level Variance LLL        (GLRLM), Gray Level Variance (GLRLM), Robust Mean Absolute        Deviation LLL, Gray Level Variance (GLDM), Variance, Mean        Absolute Deviation, Cluster Prominence, Sum Entropy LLL,        Interquartile Range LLL, Gray Level Variance LLL (GLSZM), Sum of        Squares, Robust Mean Absolute Deviation, and Sum Entropy; and        cluster 9 consists of Size Zone Non Uniformity LLL.

Clause 7. The method of clause 2, wherein:

-   -   cluster 1 consists of Short Run High Gray Level Emphasis, High        Gray Level Emphasis, and High Gray Level Run Emphasis;    -   cluster 2 consists of Skewness, Skewness LLL, Kurtosis, 90th        Percentile, Median LLL, Kurtosis LLL, and Median;    -   cluster 3 consists of Run Entropy, Run Entropy LLL, and Mean        LLL;    -   cluster 4 consists of Small Area Low Gray Level Emphasis, Low        Gray Level Zone Emphasis, and Gray Level Variance (GLSZM);    -   cluster 5 consists of Zone Entropy, Gray Level Non Uniformity        Normalized (GLRLM), and Uniformity;    -   cluster 6 consists of Zone Entropy HHH;    -   cluster 7 consists of Strength;    -   cluster 8 consists of Cluster Tendency LLL, Cluster Tendency,        Mean Absolute Deviation LLL, Gray Level Variance LLL (GLDM),        Variance LLL, Gray Level Variance LLL (GLRLM), Robust Mean        Absolute Deviation LLL, Gray Level Variance LLL (GLSZM),        Interquartile Range LLL, Sum Entropy LLL, Gray Level Variance        (GLRLM), Variance, Gray Level Variance (GLDM), Mean Absolute        Deviation, Sum Entropy, Robust Mean Absolute Deviation,        Interquartile Range, Entropy LLL, 10th Percentile LLL, 10th        Percentile, Entropy, Uniformity LLL, Gray Level Non Uniformity        Normalized LLL (GLDM), Gray Level Non Uniformity Normalized LLL        (GLRLM), Root Mean Squared, Gray Level Non Uniformity Normalized        (GLDM), Root Mean Squared LLL, and Long Run Low Gray Level        Emphasis; and    -   cluster 9 consists of Size Zone Non Uniformity LLL, Busyness,        and Size Zone Non Uniformity.

Clause 8. The method of clause 1, wherein the at least two radiomicfeatures are selected from: Median LLL, Mean LLL, Median, Root MeanSquared LLL, Mean, Kurtosis, Root Mean Squared, Run Entropy LLL (GLRLM),Uniformity, 90th Percentile, Gray Level Non-Uniformity Normalized(GLRLM), Uniformity LLL, Skewness, Gray Level Non-Uniformity NormalizedLLL (GLRLM), 10th Percentile LLL, Skewness LLL, 10th Percentile,Entropy, Interquartile Range LLL, Robust Mean Absolute Deviation LLL,Run Entropy (GLRLM), Interquartile Range, Sum Entropy (GLCM), Gray LevelNon-Uniformity Normalized LLL (GLRLM), Dependence Non-Uniformity LHL(GLDM), Kurtosis LLL, Run Length Non-Uniformity HHL (GLRLM), EntropyLLL, Robust Mean Absolute Deviation, Sum Entropy LLL (GLCM), 90thPercentile LLL, Run Entropy HHL (GLRLM), Energy, Energy LLL, Strength(NGTDM), Autocorrelation (GLCM), Mean Absolute Deviation LLL, High GrayLevel Emphasis (GLDM), Joint Average (GLCM), Sum Average (GLCM), ShortRun High Gray Level Emphasis (GLRLM), Energy HHH, High Gray Level RunEmphasis (GLRLM), Run Entropy HHH (GLRLM), Energy HHL, and Mean AbsoluteDeviation.

Clause 9. The method of any one of clauses 2 to 7, wherein the at leasttwo radiomic features are selected from the radiomic features ofclusters 1 to 8.

Clause 10. The method of any one of clauses 2 to 7, wherein the at leasttwo radiomic features are selected from the radiomic features ofclusters 1 to 7.

Clause 11. The method of any one of clauses 2 to 7, wherein the at leasttwo radiomic features are selected from the radiomic features ofclusters 1 to 6.

Clause 12. The method of any one of clauses 2 to 7, wherein the at leasttwo radiomic features are selected from the radiomic features ofclusters 1 to 5.

Clause 13. The method of any one of clauses 2 to 7, wherein the at leasttwo radiomic features are selected from the radiomic features ofclusters 1 to 4.

Clause 14. The method of any one of clauses 2 to 7, wherein the at leasttwo radiomic features are selected from the radiomic features ofclusters 1 to 3.

Clause 15. The method of any one of clauses 2 to 7, wherein the at leasttwo radiomic features are selected from the radiomic features ofclusters 1 and 2.

Clause 16. The method of any one of clauses 1 to 14, wherein the atleast two radiomic features comprises at least three radiomic features.

Clause 17. The method of any one of clauses 1 to 13, wherein the atleast two radiomic features comprises at least four radiomic features.

Clause 18. The method of any one of clauses 1 to 12, wherein the atleast two radiomic features comprises at least five radiomic features.

Clause 19. The method of any one of clauses 1 to 11, wherein the atleast two radiomic features comprises at least six radiomic features.

Clause 20. The method of any one of clauses 1 to 10, wherein the atleast two radiomic features comprises at least seven radiomic features.

Clause 21. The method of any one of clauses 1 to 9, wherein the at leasttwo radiomic features comprises at least eight radiomic features.

Clause 22. The method of any one of clauses 1 to 8, wherein the at leasttwo radiomic features comprises at least nine radiomic features.

Clause 23. The method of clause 1, wherein the at least two radiomicfeatures comprises six radiomic features, wherein the six radiomicfeatures are Short Run High Gray Level Emphasis, Skewness, Run Entropy,Small Area Low Gray Level Emphasis, Zone Entropy HHH, and Zone Entropy.

1. A method for characterising a perivascular region using medicalimaging data of a subject, the method comprising calculating the valueof a radiomic signature of the perivascular region using the medicalimaging data; wherein the radiomic signature is calculated on the basisof measured values of at least two radiomic features of the perivascularregion, the measured values of the at least two radiomic features beingcalculated from the medical imaging data.
 2. The method of claim 1,wherein the radiomic signature provides a measure of the texture of theperivascular region.
 3. The method of any preceding claim, wherein theradiomic signature is predictive of cardiovascular risk, optionallywherein the radiomic signature is predictive of the likelihood of thesubject experiencing a major adverse cardiovascular event.
 4. The methodof any preceding claim, wherein at least one of the at least tworadiomic features is calculated from a wavelet transformation of theattenuation values.
 5. The method of any preceding claim, wherein the atleast two radiomic features are selected from the radiomic features ofclusters 1 to 9, wherein the at least two radiomic features are eachselected from different clusters, wherein: cluster 1 consists of ShortRun High Gray Level Emphasis, High Gray Level Emphasis, High Gray LevelRun Emphasis, Autocorrelation, Sum Average, Joint Average, and High GrayLevel Zone Emphasis; cluster 2 consists of Skewness, Skewness LLL,Kurtosis, 90th Percentile, 90th Percentile LLL, Median LLL, KurtosisLLL, and Median; cluster 3 consists of Run Entropy, Dependence EntropyLLL, Dependence Entropy, Zone Entropy LLL, Run Entropy LLL, and MeanLLL; cluster 4 consists of Small Area Low Gray Level Emphasis, Low GrayLevel Zone Emphasis, Short Run Low Gray Level Emphasis, Low Gray LevelRun Emphasis, Low Gray Level Emphasis, Small Dependence Low Gray LevelEmphasis, Gray Level Variance LLL (GLSZM), Gray Level Variance (GLDM),Variance, Gray Level Variance (GLDM), Difference Variance LLL, GrayLevel Variance LLL (GLRLM), Variance LLL, Gray Level Variance LLL(GLDM), Sum of Squares, Contrast LLL, Mean Absolute Deviation,Interquartile Range, Robust Mean Absolute Deviation, Long Run Low GrayLevel Emphasis, Difference Variance, Gray Level Variance (GLSZM),Inverse Difference Moment Normalized, Mean Absolute Deviation LLL, Sumof Squares LLL, and Contrast; cluster 5 consists of Zone Entropy, GrayLevel Non Uniformity Normalized (GLRLM), Gray Level Non UniformityNormalized LLL (GLRLM), Sum Entropy, Joint Energy, Entropy, Gray LevelNon Uniformity Normalized (GLDM), Joint Energy, Gray Level NonUniformity Normalized LLL (GLDM), Uniformity LLL, Sum Entropy LLL, andUniformity; cluster 6 consists of Zone Entropy HHH, Size Zone NonUniformity Normalized HHH, and Small Area Emphasis HHH; cluster 7consists of Strength, Coarseness HLL, Coarseness, Coarseness LHL,Coarseness LLL, Coarseness LLH, Coarseness HHH, Coarseness HLH,Coarseness HHL, and Coarseness LHH; cluster 8 consists of ClusterTendency LLL, Cluster Tendency, Sum of Squares LLL, Mean AbsoluteDeviation LLL, Gray Level Variance LLL (GLDM), Variance LLL, Gray LevelVariance LLL (GLRLM), Gray Level Variance (GLRLM), Robust Mean AbsoluteDeviation LLL, Gray Level Variance (GLDM), Variance, Mean AbsoluteDeviation, Cluster Prominence, Sum Entropy LLL, Interquartile Range LLL,Gray Level Variance LLL (GLSZM), Sum of Squares, Robust Mean AbsoluteDeviation, Sum Entropy, Interquartile Range, Cluster Prominence LLL,Entropy LLL, 10th Percentile LLL, 10th Percentile; and cluster 9consists of Size Zone Non Uniformity LLL, Dependence Non Uniformity HLL,Gray Level Non Uniformity HLL (GLSZM), Gray Level Non Uniformity(GLSZM), Run Length Non Uniformity HHL, Run Length Non Uniformity LHL,Dependence Non Uniformity LHL, Dependence Non Uniformity, Run Length NonUniformity HLH, Busyness, Run Length Non Uniformity LLH, Dependence NonUniformity LLH, Dependence Non Uniformity LLL, Size Zone Non Uniformity,Energy HLL, Run Length Non Uniformity LHH, Size Zone Non Uniformity HLL,Gray Level Non Uniformity LLH (GLSZM), Gray Level Non Uniformity LHL(GLSZM), Gray Level Non Uniformity LLL (GLSZM), Run Length NonUniformity HLL, Gray Level Non Uniformity HLH (GLSZM), Gray Level NonUniformity HHL (GLSZM), Run Length Non Uniformity, and Run Length NonUniformity HHH.
 6. The method of any one of claims 1 to 4, wherein theat least two radiomic features are selected from: Median LLL, Mean LLL,Median, Root Mean Squared LLL, Mean, Kurtosis, Root Mean Squared, RunEntropy LLL (GLRLM), Uniformity, 90th Percentile, Gray LevelNon-Uniformity Normalized (GLRLM), Uniformity LLL, Skewness, Gray LevelNon-Uniformity Normalized LLL (GLRLM), 10th Percentile LLL, SkewnessLLL, 10th Percentile, Entropy, Interquartile Range LLL, Robust MeanAbsolute Deviation LLL, Run Entropy (GLRLM), Interquartile Range, SumEntropy (GLCM), Gray Level Non-Uniformity Normalized LLL (GLRLM),Dependence Non-Uniformity LHL (GLDM), Kurtosis LLL, Run LengthNon-Uniformity HHL (GLRLM), Entropy LLL, Robust Mean Absolute Deviation,Sum Entropy LLL (GLCM), 90th Percentile LLL, Run Entropy HHL (GLRLM),Energy, Energy LLL, Strength (NGTDM), Autocorrelation (GLCM), MeanAbsolute Deviation LLL, High Gray Level Emphasis (GLDM), Joint Average(GLCM), Sum Average (GLCM), Short Run High Gray Level Emphasis (GLRLM),Energy HHH, High Gray Level Run Emphasis (GLRLM), Run Entropy HHH(GLRLM), Energy HHL, and Mean Absolute Deviation.
 7. The method of anypreceding claim, wherein the at least two radiomic features are selectedfrom the radiomic features of clusters 1 to
 6. 8. The method of anypreceding claim, wherein the at least two radiomic features comprises atleast six radiomic features.
 9. The method of any preceding claim,further comprising predicting the risk of the subject experiencing amajor adverse cardiac event based on at least the calculated value ofthe radiomic signature.
 10. The method of any preceding claim, furthercomprising determining whether the subject has vascular disease orcoronary heart disease based on at least the calculated value of theradiomic signature, or wherein the calculated value of the radiomicsignature is used to discriminate unstable from stable coronary lesions.11. A method for deriving a radiomic signature for predictingcardiovascular risk, the method comprising using a radiomic dataset toconstruct a perivascular radiomic signature for predictingcardiovascular risk, the radiomic signature being calculated on thebasis of at least two radiomic features of a perivascular region;wherein the dataset comprises the values of a plurality of radiomicfeatures of a perivascular region obtained from medical imaging data foreach of a plurality of individuals, the plurality of individualscomprising a first group of individuals having reached a clinicalendpoint indicative of cardiovascular risk within a subsequent periodafter the collection of the medical imaging data and a second group ofindividuals having not reached a clinical endpoint indicative of cardiovascular risk within the subsequent period.
 12. The method of claim 11,further comprising identifying significant radiomic features fromamongst the plurality of radiomic features that are each significantlyassociated with the clinical endpoint, the at least two radiomicfeatures each being selected to be, or to be collinear with, differentsignificant radiomic features.
 13. The method of claim 12, furthercomprising identifying a subset of the significant radiomic featuresthat are not collinear with each other, the at least two radiomicfeatures each being selected to be, or to be collinear with, differentradiomic features belonging to the subset.
 14. The method of claim 11,wherein each of the at least two radiomic features is selected to becollinear with a corresponding partner radiomic feature that issignificantly associated with the clinical endpoint, the partnerradiomic features of the at least two radiomic features each beingdifferent to one another, optionally wherein each of the partnerradiomic features is selected to be not collinear with any of the otherpartner radiomic features, and further optionally wherein at least oneof the at least two radiomic features is its own partner radiomicfeature.
 15. The method of any one of claims 11 to 14, wherein themethod comprises identifying a plurality of clusters of radiomicfeatures, each cluster comprising a subset of the plurality of radiomicfeatures, wherein each cluster comprises an original radiomic featurewith which each of the other radiomic features in that cluster isselected to be collinear, and wherein the at least two radiomic featuresare each selected from different clusters, optionally wherein each ofthe original radiomic features is selected to be not collinear with anyof the original radiomic features of any of the other clusters.
 16. Themethod of any one of claims 11 to 15, wherein the at least two radiomicfeatures are selected to be not collinear with each other.
 17. Themethod of any one of claims 11 to 16, wherein the radiomic signature isconstructed to be correlated with the clinical endpoint, optionallywherein the radiomic signature is constructed to be significantlyassociated with the clinical endpoint.
 18. The method of any one ofclaims 11 to 17, wherein the at least two radiomic features are selectedto be stable.
 19. The method of any one of claims 11 to 18, wherein thestep of constructing the radiomic signature is performed using a machinelearning algorithm.
 20. The method of any one of claims 11 to 19,wherein the radiomic signature is constructed to provide a measure ofthe texture of the perivascular region.
 21. The method of any one ofclaims 11 to 20, further comprising configuring a system for calculatingthe value of the radiomic signature for a patient.
 22. The method of anyone of claims 11 to 21, further comprising characterising a perivascularregion of a patient by calculating the value of the radiomic signaturefor the perivascular region of the patient.
 23. The method of anypreceding claim, wherein the perivascular region comprises perivascularadipose tissue.
 24. The method of any preceding claim, wherein theradiomic signature is calculated on the basis of further radiomicfeatures of the perivascular region in addition to the at least tworadiomic features.
 25. A system configured to perform the method of anyone of claims 1 to 24.